mr 1 and mr 2

in eah path they travel 4 horizontal and 4 vertical steps so 4H and 4V can be permuted in $\frac{8!}{4!*4!}$ and both can happen in (8!/4!*4! )squared from product rule .so this is sample space.they meet in points which are at a equal distance from mr 1 and 2 starting points.their are 5 such points lying on the line which is 2 units from mr 1 and 2 starting points.from each points they can reach their destiny in same way .