This problem combines LCA and Euler Tour. First, use binary lifting to find the ancestor of v at depth h. Call this ancestor a.
Now you need to count nodes at depth d inside a's subtree. Use Euler Tour to flatten a's subtree into a range. Then count how many nodes in that range have depth exactly d.
You can preprocess this with a data structure (like a map of depth → sorted list of Euler Tour positions) to answer each query in .
Space complexity is for the data structures used.