This one has what we call a “clause of fearing.” As you might assume, you see such constructions with words like “timeo.”
The way to handle these sorts of sentences is to think of them as two parts, with a verb in each part.
First you have, “timeo”. Simple enough. “I’m afraid.”
Second you have “ne abeas.” Depending on how much you’ve studied the subjunctive, this may or may not make sense to you on its own. I’m guessing that it doesn’t, otherwise you may have been able to figure out the original sentence. You can use the subjunctive by itself (without any other clauses, like when you have a “cum” clause) for orders or prohibitions. This is called a “jussive,” which is to say that it’s an order (from “iubeo, iubere, iussi, iussus”). When you want to forbid something, you use a “ne” instead of “non” (generally, use “ne” with subjunctives).
Jussives:
[Ut] Abeas! go away!
Ne abeas! Don’t go away!
You can get also have jussives in the third person (Abeat! Let him go away!) and first person (abeamus! Let’s go away!).
Now put the two parts together: timeo! ne abeas! I’m afraid! Don’t go away! Or, taken as one sentence this becomes “I’m afraid that you will go away.” (You see that in clauses of fearing you don’t have a accusative+infinitive construction like with “dico eum abire” “I says that he goes”.) Try to think of what the person is afraid of (that the other person will leave), and then you should be able to make sense of it.
Now to take this a step further, let’s say you’re afraid that someone WON’T go away. As with jussives, there is a construction with the subjunctive for wishing that something happens, the difference being that you use “ut”. “ut abeat!” “[Oh!] may/that he go away!” Now when you combine with timeo you get, “timeo! ut abeat!” I’m afraid! may/that he go away! In normal language this becomes “timeo ut abeat” “I’m afraid that he won’t go away”! The won’t sneaks in here because the person and wants something to leave, so he’s afraid that it won’t go away.
I don’t know if this all makes sense, but I hope it helps you with your test in some way.