Here is a definition using recursion.
int leftHeight(const Node* t) { if(t == NULL) return 0; else return 1 + leftHeight(t->left); }
Here is a definition using a loop. This one is simple using a loop because you only need to look one direction in the tree (to the left).
int leftHeight(const Node* t) { const Node* r = t; int count = 0; while(r != NULL) { r = r->left; count++; } return count; }
Note. Variable r needs to have type const Node*, indicating that r can be made to point to different nodes but that the node pointed to by r cannot be changed.