"Her " would be only talking Anna (so this isnt your answer)
"His" would be only talking about Paul (so this isnt your answer either)
"They" wouldn't be your answer because it would sound right if your sentence was 'Anna and Paul bought they hamsters to class for pet day ' that's why it is wrong.
So, therefore your answer that completes this sentence would have to be "Their (option C.)"
Good Luck!