"Grandmother wears socks and shoes."
Translation:할머니께서 양말하고 신발을 신으세요.
I've seen in comments from other questions that the difference between 와/과 and 하고 has to do with the relatedness of the things in question. One of them means the two things are presented together and the other means that they are not closely tied, but are being mentioned together. Like "I ate cereal and milk" would be one of them because it implies they were eaten as one thing and "I bought cereal and milk" is the other because cereal and milk are unrelated separate items when purchased at the store.