Assuming that we have the following SNP and phenotype data, is the SNP significantly associated with the phenotype?
Your approach is correct - it's not the only one permitted under their conditions, but it would be the standard way given only that information.

F-test compares a "full model" (predicting the phenotype using genotype and an intercept) versus a "reduced model" (predicting the phenotype using only the intercept, i.e. the mean value of phenotype). The p-value tells whether the full model predicts better, i.e. whether adding the genotype variable significantly improves the prediction. In this single-variable case, it should be approximately equal to the p-value for the beta coefficient of the genotype, if that's more familiar.

Anyway, this isn't specific to genetics, so you can check out other online sources - e.g. https://onlinecourses.science.psu.edu/stat501/node/295 for a longer, but accessible explanation of the F-test, and https://stats.stackexchange.com/ for many answers to similar questions.