b) Again using your notation. I'm choosing a +x direction in the direction of the vector X and a +y direction in the direction of +y.
As you correctly noted:
So X = T = (1/4)W and Y = W - R = W - (7/8)W = (1/8)W using the results of part a.
Now, Y is a static friction force which is only as large as it needs to be to hold the ladder up. If I assume that static friction is at its maximum, then the value of that I calculate would be the minimum value we would require to hold the ladder up. (Note: X is the normal force at this point.)
Solving this for gives a value of 1/2. Thus