Focus on triangles ABC and ABD. They are both right triangles, and angle CAB has the same measure of angle BAD (because AB is the bisector).
This implies that angles ABC and ABD have the same measure, because they are complementary to BAC and BAD, respectively.
So, triangles ABC and ABD have the same angles, and thus they are at least similar, if not congruent.
But they share the side AB, so they actually are congruent, and sides BC and BD have the same length:
[tex]6y-16=4y+6 \iff 2y=22 \iff y=11[/tex]
So, the length of BC is
[tex]BC=6y-16=6\cdot 11 - 16 = 66-16=50[/tex]
