Question

my sister has hairy knuckles; she likes to comb them when shes bored.
correct use of a semicolon
incorrect use of a semicolon

Explanation:

A semicolon is used correctly when separating two independent clauses (complete sentences) that are related in meaning. The two parts "My sister has hairy knuckles" and "she likes to comb them when she's bored" are both independent clauses and are related, so the semicolon use is correct.

Answer:

correct use of a semicolon