Random Problem you can do when you're bored

You don't have to explain I know the answer:

 

How many ways are there to walk from  to  by only moving rightward or upward?

 

[asy]

draw((0,0)--(2,0)--(2,6)--(6,6));
draw((0,0)--(0,3)--(6,3)--(6,6));

draw((0,1)--(2,1));
draw((0,2)--(2,2));
draw((1,0)--(1,3));
draw((3,6)--(3,3));
draw((4,6)--(4,3));
draw((5,6)--(5,3));
draw((2,4)--(6,4));
draw((2,5)--(6,5));

label("$A$",(0,0),SW);
label("$B$",(6,6),NE);
[/asy]