Note that this is a two to one mapping, Y is defined on (0,16).
I'll derive it, but it's just like the squaring of a st normal to get a chi-square.
here's the algebra involving the 2-1 mapping
If you differentiate, which is not necessary, you get the sum of the two solutions TIMES the jacobian.
AND when 0<y<16 we get................
If y is outside that region you get zero.