Susan doesn’t want to you with her problems.*
inform
defame
worry
wary

Susan doesn't want to worry you with her problems. 
First of all, you need a verb in this sentence, so you can immediately rule out wary because it is only an adjective (and plus it means cautious, so it doesn't fit here). Inform means to notify, so it's not correct either. Defame means to damage someone's reputation so it obviously doesn't belong here either.

The correct answer, in my opinion, is C. worry. "Inform" has too neutral a meaning to be employed in this context. "Defame" means slander, denigrate, libel, smear - so it makes no sense in this sentence. On the other hand, "wary" is an adjective that means cautious, distrustful, suspicious, so it also makes no sense. Susan is just considerate, so she doesn't want to cause other people to worry because of her problems.