How can I rewrite this? What I did wasn't right, so I was wondering if there was another way to rewrite it. It's in 6/8.
Hmm. As I mentioned in the comments, your answer looks perfectly correct to me:
I could potentially imagine someone suggesting you break the initial quarter rest into two eighth notes, but in my experience this is unnecessary and too cluttered:
The only other possibility I can imagine for 6/8 is if they are requesting vocal notation, where we typically don't beam the notes together unless they are to be sung with the same syllable. As such, something like this may have been intended:
Otherwise, if this was to be written in 6/8, your given solution should be correct.
I'd think that if this 6/8 were to be "in three", then the first quarter-rest is fine, and then the next two eighth notes should be barred together, and then the two sixteenths and the last eighth.
If it's "in 2", then the first eighth should be separate, and the rest barred-together. Replacing the quarter-rest by two eighth-rests might be helpful, and consonant with the situation, and I'd do it, but I don't think it's mandatory... :)
If I didn't know whether it was to be "in two" or "in three", then I'd not know about optimizing the notation.