This is a nice question. You know how to solve these problems with stars and bars, I gather. So we want to know how many ways there are to put $28$ indistinguishable balls in $4$ distinct buckets, with at least $-10$ and no more than $20$ balls in each bucket. Start out by putting $-10$ balls in each bucket -- difficult in the real world, but no trouble at all in math. Now we have $-40$ balls, so to get up to $28$ we need to add $68$ balls to the buckets. Since we aren't allowed to have more than $20$ balls in a bucket, we can't place any more than $30$ balls in a bucket.
So the question is transformed into, "In how many ways can $68$ indistinguishable balls be placed in $4$ distinct buckets, with no more than $30$ balls in a single bucket?"
Take it from here.