The total number of ways to get from (0,0) to (4,6) as learned in basic counting is 4 + 6 choose 4. 10 choose 4 = 210.
The number of ways to get from (0,0) to (2,4) is 6 choose 2, and the ways to get from (2,4) to (4,6) is 4 choose 2. Total ways is 15 * 6 = 90
Why calculate that? So now we can know the total number of ways to get their, and the total number of ways to get from the origin to (4,6) that pass through the frog and subtract the two totals.
210 - 90 = 120 total ways Marvin can reach his home.