In how many ways cam we reach from the point $(0,0,0)$ to point $(3,7,11)$ in space where the movement is possible only along the x-axis or z-axis or parallel to them and change of axes is permitted only at integral points? An integral point is a point whose coordinates are integers.
Sorry for not taking an approach as I am unable to understand how y-coordinate is changing when movement is not possible along y axis.
Here you can find some descriptions of what you want.
and you can discover the definition of NP-hardness. Also you can proceed further for other classes of problems such as P or NP class problems. Hope they help!