Find the number of paths from P to Q, where each step is to the right or up.
There are 6*24 = 144 paths from P to Q.
To get from P to the midddle is a total of 5 steps, 3 up and 2 across
So that is 5!/(2!3!) ways
now do the same for the second bit and then multiply the two together.
Please let locki finish it him/herself