The optimization process and recommendations:

1. Avoid Subqueries (query line: 16): We advise against using subqueries as they are not optimized well by the optimizer. Therefore, it's recommended to join a newly created temporary table that holds the data, which also includes the relevant search index.
2. Avoid Subqueries (query line: 27): We advise against using subqueries as they are not optimized well by the optimizer. Therefore, it's recommended to join a newly created temporary table that holds the data, which also includes the relevant search index.
3. 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.
4. Prefer IN Clause Over OR Conditions (modified query below): Using an IN clause is far more efficient than OR conditions, when comparing a column to more than one optional values. When using an IN clause, the database sorts the list of values and uses a quick binary search.

Optimal indexes for this query:

ALTER TABLE `product_nutrition_facts` ADD INDEX `product_facts_idx_nutrition_id_nutrition_value` (`nutrition_id`,`nutrition_value`);
ALTER TABLE `products_info` ADD INDEX `products_info_idx_brand_product_id` (`brand`,`product_id`);

The optimized query:

SELECT
        DISTINCT p.product_id,
        p.brand,
        p.e_name,
        p.image_low 
    FROM
        products_info p 
    JOIN
        product_nutrition_facts pn 
            ON p.product_id = pn.product_id 
    WHERE
        p.brand = 'AL MARAI' 
        AND (
            (
                p.product_id IN (
                    SELECT
                        pn.product_id 
                    FROM
                        product_nutrition_facts pn 
                    WHERE
                        pn.nutrition_id = 3 
                        AND pn.nutrition_value <= 15
                )
            ) 
            AND (
                p.product_id IN (
                    SELECT
                        pn.product_id 
                    FROM
                        product_nutrition_facts pn 
                    WHERE
                        pn.nutrition_id = 4 
                        AND pn.nutrition_value <= 140
                )
            )
        ) 
        AND (
            pn.nutrition_id IN (
                3, 4
            )
        )