This is straightforward. The nodes of the given tree are given in square boxes. The weights associated with the nodes are the numbers example $15,9,10$ etc.
Weighted path length = sigma(for(each node in the tree) (path length)*(weight of the node) ).
= $\sum_{i=1}^{n} PathLength_{i} * Weight Of Node_{i} $
So answer (written in path_length*weight form)$ = 4*2 + 4*4 + 4*5 + 4*7 + 3*9 + 3*10 + 1*15 = \mathbf{144}$