You start at the black field bottom left and have to move op til top right black field by only move right and up. What is the probability for moving over the white field with the cross in your way to the black field?
By using binomial coefficient I get that the probability is $\frac{35^2}{3432}$. Is that correct?
The total amount of ways to go from the bottom left square to the top right is $\binom{14}{7}=3432$. The amount of ways to go from the bottom left square to the top right that go through the cross is the amount of ways to go from the bottom left to the cross multiplied by the amount of ways to go from the cross to the top left, i.e. $\binom{7}{3}\times\binom{7}{3}=1225(=35^2)$.
So you are right, the probability is $\frac{35^2}{3432}$