The number of ways of getting to a node is the sum of the number of ways of getting to the nodes immediately to the left and below the current node.

(if the node is on the boundary it is the same as its one node either to its left or below it).

So just label each node in the diagram with the corresponding sum, with the bottom left node initially set at 1 to get what is shown in the attachment:

So we see the answer is 128 - or it would be if there wasn't an error in my arithmetic, but there is so it ain't.

If you do the arithmetic correctly you will find the answer is 132

RonL