What are the number of paths from $(1, 0)$ to $(7, 6)$ without crossing the diagonal?

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I am not able to apply this in the formula.I tried putting in the catalan formula but it is for(n,n) you are allowed to move up and down. you can touch the diagonal but can't cross it.

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You are moving six cells up and six cells right. Assuming the diagonal of interest is from $(1,0)$ to $(7,6)$ your problem is the classic one with the Catalan number solution, just positioned one cell up on the lattice. If the diagonal of interest is from $(0,0)$ to $(6,6)$ there are more possibilities. You would have to think about how many ways there are to touch the diagonal below.