The optimization process and recommendations:

1. Avoid Selecting Unnecessary Columns (query line: 2): Avoid selecting all columns with the '*' wildcard, unless you intend to use them all. Selecting redundant columns may result in unnecessary performance degradation.
2. 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.

Optimal indexes for this query:

ALTER TABLE `attribute_values` ADD INDEX `attribute_values_idx_value_id_id` (`value_id`,`ID`);
ALTER TABLE `products` ADD INDEX `products_idx_id` (`ID`);

The optimized query:

SELECT
        DISTINCT P.* 
    FROM
        attribute_product_values APV 
    INNER JOIN
        products P 
            ON P.ID = APV.product_id 
    LEFT JOIN
        attribute_values AV 
            ON AV.ID = APV.attribute_value_id 
            AND AV.value_id = 6 
    LEFT JOIN
        attribute_values AV2 
            ON AV2.ID = APV.attribute_value_id 
            AND AV2.value_id = 3 
    WHERE
        AV.ID IS NOT NULL 
        OR AV2.ID IS NOT NULL