Path of exact cost k in DAG
When you get a question about a DAG, the first thing to do is a topological sort.

Now, go through all vertexes in order. For each vertex $v$, keep all the possible costs of a path from $s$ to $v$; there will be no more than $3V$ distinct costs. For each edge $e(v,u)$, add to $u$ the costs of $v$ + the weight of $e$.