In deciding how to analyze your experimental design, you'll want to consider the specifics of the design itself, particularly the number of factors and the type of samples used.
Looking at the question, we can determine that the experimental design has two factors, and that both factors are tested using related samples.
In the field of statistics, analyzing the variance, or ANOVA, is usually performed to compare the means of three or more independent (unrelated) groups.
When we have related or dependent samples and we're analyzing an experimental design with two factors simultaneously, the design is usually analyzed with a specific type of ANOVA, known as a two-way within-subjects ANOVA.
A two-way within-subjects ANOVA, also known as a two-way repeated measures ANOVA, is used when you have repeated measures on the same subjects under different conditions. Two ways refers to the two factors in your design, and within subjects means that each subject experienced every level of each factor.
Thus, in light of the provided information, the appropriate statistical test for this kind of experimental design is option 'A', a two-way within-subjects Analysis of Variance. This type of analysis will allow us to determine any significant difference between the means considering the two factors, also helping to identify any interactions between them.