HMMT 2025 C4

Sophie is at $(0,0)$ on a coordinate grid and would like to get to $(3,3)$ . If Sophie is at $(x,y)$ , in a single step she can move to one of $(x + 1,y)$ , $(x,y + 1)$ , $(x - 1,y + 1)$ , or $(x + 1,y - 1)$ . She cannot revisit any points along her path, and neither her $x$ - coordinate nor her $y$ - coordinate can ever be less than 0 or greater than 3. Compute the number of ways for Sophie to reach $(3,3)$ .