For your research questions, you can use a mixed-design ANOVA with gender as the between-subjects factor and valence (positive vs. negative) as the within-subjects factor. The dependent variable would be the number of words recalled correctly.
In this design, gender would be your independent variable (between-subjects factor) and valence of the word (positive or negative) would be your independent variable (within-subjects factor). The dependent variable would be the number of words recalled correctly.
You can use a mixed-design ANOVA because it allows you to analyze the effects of both the between-subjects factor (gender) and within-subjects factor (word valence) on the dependent variable (number of words recalled correctly).
You can then follow up with post-hoc tests (such as t-tests or pairwise comparisons) to further examine any significant effects found in the ANOVA.
I recommend including 'neutral' words in addition to 'positive' and 'negative' words as a baseline. Be sure to also match positive and negative words with respect to number of letters, frequency, etc,.