The optimization process and recommendations:

1. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.
2. Explicitly ORDER BY After GROUP BY (modified query below): By default, the database sorts all 'GROUP BY col1, col2, ...' queries as if you specified 'ORDER BY col1, col2, ...' in the query as well. If a query includes a GROUP BY clause but you want to avoid the overhead of sorting the result, you can suppress sorting by specifying 'ORDER BY NULL'.
3. Remove Redundant Left Joins (modified query below): Redundant LEFT JOINs (e.g. `mage_review_entity_summary`) were detected in the query. Removing them will result in a performance improvement. In some cases, JOINs become redundant after an optimization is applied, such as when converting OR conditions to a UNION clause.
4. Use Numeric Column Types For Numeric Values (query line: 13): Referencing a numeric value (e.g. 2) as a string in a WHERE clause might result in poor performance. Possible impacts of storing numbers as varchars: more space will be used, you won't be able to perform arithmetic operations, the data won't be self-validated, aggregation functions like SUM won't work, the output may sort incorrectly and more. If the column is numeric, remove the quotes from the constant value, to make sure a numeric comparison is done.
5. Use Numeric Column Types For Numeric Values (query line: 17): Referencing a numeric value (e.g. 1) as a string in a WHERE clause might result in poor performance. Possible impacts of storing numbers as varchars: more space will be used, you won't be able to perform arithmetic operations, the data won't be self-validated, aggregation functions like SUM won't work, the output may sort incorrectly and more. If the column is numeric, remove the quotes from the constant value, to make sure a numeric comparison is done.
6. Use Numeric Column Types For Numeric Values (query line: 22): Referencing a numeric value (e.g. 154) as a string in a WHERE clause might result in poor performance. Possible impacts of storing numbers as varchars: more space will be used, you won't be able to perform arithmetic operations, the data won't be self-validated, aggregation functions like SUM won't work, the output may sort incorrectly and more. If the column is numeric, remove the quotes from the constant value, to make sure a numeric comparison is done.
7. Use Numeric Column Types For Numeric Values (query line: 25): Referencing a numeric value (e.g. 70) as a string in a WHERE clause might result in poor performance. Possible impacts of storing numbers as varchars: more space will be used, you won't be able to perform arithmetic operations, the data won't be self-validated, aggregation functions like SUM won't work, the output may sort incorrectly and more. If the column is numeric, remove the quotes from the constant value, to make sure a numeric comparison is done.
8. Use Numeric Column Types For Numeric Values (query line: 30): Referencing a numeric value (e.g. 153) as a string in a WHERE clause might result in poor performance. Possible impacts of storing numbers as varchars: more space will be used, you won't be able to perform arithmetic operations, the data won't be self-validated, aggregation functions like SUM won't work, the output may sort incorrectly and more. If the column is numeric, remove the quotes from the constant value, to make sure a numeric comparison is done.
9. Use Numeric Column Types For Numeric Values (query line: 31): Referencing a numeric value (e.g. 1) as a string in a WHERE clause might result in poor performance. Possible impacts of storing numbers as varchars: more space will be used, you won't be able to perform arithmetic operations, the data won't be self-validated, aggregation functions like SUM won't work, the output may sort incorrectly and more. If the column is numeric, remove the quotes from the constant value, to make sure a numeric comparison is done.

Optimal indexes for this query:

ALTER TABLE `mage_catalog_category_product_index` ADD INDEX `mage_category_idx_store_categor_product_visibil` (`store_id`,`category_id`,`product_id`,`visibility`);
ALTER TABLE `mage_catalog_product_index_eav` ADD INDEX `mage_product_idx_attribu_store_entity_value` (`attribute_id`,`store_id`,`entity_id`,`value`);
ALTER TABLE `mage_catalog_product_index_price` ADD INDEX `mage_product_idx_website_id_customer_entity_id` (`website_id`,`customer_group_id`,`entity_id`);

The optimized query:

SELECT
        `width_idx`.`value`,
        COUNT(DISTINCT width_idx.entity_id) AS `count` 
    FROM
        `mage_catalog_product_flat_1` AS `e` 
    INNER JOIN
        `mage_catalog_category_product_index` AS `cat_index` 
            ON cat_index.product_id = e.entity_id 
            AND cat_index.store_id = 1 
            AND cat_index.visibility IN (
                2,
            4) 
            AND cat_index.category_id = '2' 
        INNER JOIN
            `mage_catalog_product_index_price` AS `price_index` 
                ON price_index.entity_id = e.entity_id 
                AND price_index.website_id = '1' 
                AND price_index.customer_group_id = 0 
        INNER JOIN
            `mage_catalog_product_index_eav` AS `gender_idx` 
                ON gender_idx.entity_id = e.entity_id 
                AND gender_idx.attribute_id = '154' 
                AND gender_idx.store_id = 1 
                AND gender_idx.value IN (
                    '70'
                ) 
        INNER JOIN
            `mage_catalog_product_index_eav` AS `width_idx` 
                ON width_idx.entity_id = e.entity_id 
                AND width_idx.attribute_id = '153' 
                AND width_idx.store_id = '1' 
        GROUP BY
            `width_idx`.`value` 
        ORDER BY
            NULL