Narges, you need to include the “of,” and with the “of” the sentence if formal and correct. The preposition “of” links to the phrase “products made by female-headed households.” Without the “of,” there is no explanation of what the photographs depicted, so the photos could be photos of anything. It may help to think of what the sentence would look like if it just discussed the photos or just the marketing: “I had responsibility for taking photos of products made by female-headed households.” “I had the responsibility for marketing products made by female-headed households.” When you combine both taking photos and marketing into one sentence, you get the sentence you wrote.

I had the responsibility of taking pictures and marketing products that were produced by female run households. (I think this is correct)