If X and Y have the joint pdf
$\displaystyle f_{X,Y}(x,y) = 2, \ \ \ 0 < x < y < 1, $
then find $\displaystyle P (0 < X < 0.5 | y = 0.75)$
find the conditional density of X given Y
First you must find the marginal of Y and divide the joint density by that marginal
When you finally have the conditional density, plug in your value for y and integrate x over the region.
HOWEVER, since the joint density is uniform over the triangle it will be uniform over the line y=.75
since you want 0<x<.5 the answer should be 2/3 which is two-thirds of that line.
DRAW the region and you will see how obvious this is.