If BX = 9 and BA = 15, we can say that the measure of AX = 6 because 15 - 9 = 6.
To solve the length of YC, we can have the following ratio:

BX = 9, XA = 6, BY = 15, YC = x
Let's plug these values to the ratio above.

Then, solve for x or the measure of YC.

Therefore, the measure of YC is 10 units.