The appropriate solution to determining the effect size for any significant effects in a two-way analysis of variance (ANOVA) is by computing Eta-squared. Eta-squared is a measure of effect size which is used in the analysis of variance. It's used to assess the magnitude of the variation in the dependent variable which is explained by the independent variable(s). It is essentially computed as the ratio of the sum of squares between the groups to the total sum of squares.
Eta-squared represented in the abbreviated letter 'n squared'. Therefore, in our options given, the correct one that matches 'n squared' is option C. Hence, the correct answer to this question is option C: 'n squared'.
By choosing 'n squared', we are saying that we compute the proportion of variance accounted for in our two-way ANOVA sample by using Eta-squared which is the measure of effect size.