Here we have three similar triangles
In similar triangles sides are in proportion
The altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse.
[tex] \frac{part of hypotenuse }{altitude} =\frac{altitude}{other part of hypotenuse} [/tex]
[tex] \frac{16}{y} =\frac{y}{4} [/tex]
We cross multiply to solve for y
[tex] y^{2} =64 [/tex]
Taking root of both sides
y=8
