We can see that triangles ABC and AXY are congruent
This means that

Now, we know that BX=10, BY=8 and BA=AX+BX, hence AX=BA-BX, we have

now, since BA-BX=15-10, BA-BX=5, it yields,

Now, we need to isolate YC, this is given by

Since

we have that

hence, the answer is YC=4, which corresponds to A).