We are to find an unknown side in a case of a triangle bisected via one of its angles.
We therefore use the bisecting angle theorem:
Which in the case of our image:
can be written as the following proportion:
8 / 4 = y / 6
in order to solve for "y", we multiply both sides by 6:
(8 * 6) / 4 = y
48 / 4 = y
then y = 12