@Abhrajyoti00Yeah answer is 10, I only considered number of paths below x = y line (for lower triangle). Same number of paths will also exists for upper triangle.

So for the above problem total number of path from $(0, 0)$ to $(n, n)$ is number of path that are below $x = y$ line + number of path that is above $x = y$ line
= $2 * C_3 = 2*5 = 10$