Another Similar Triangles Question

A segment drawn parallel to the base of a triangle splits the sides proportionately

In triangle AXC....since  segment ZY  is parallel to base XC..so...

XZ : ZA  = YC : AY

4 : 8  = YC  : AY

1 : 2  =  YC : AY 

And in triangle ABC.....segment XY  is parallel to base BC...so...

BX :  AX =  YC  : AY

So

BX : AX  = 1 : 2

BX : [  XZ + ZA ]  = 1 : 2

BX /  [ 4 + 8 ]  = 1 : 2

BX / 12  = 1 : 2

So  BX  =  6

Thank you Chris