The triangle DCP in the figure is similar to the triangle PBE.

So there is DC: CP = Pb: Be.

Then 8/x=( 12-x)/y

Then y = (12-x) * x/8 =-(x-6) * (x-6)/8+4.5.

The relationship between y and x is y=-(x-6)*(x-6)/8+4.5.

When x=6, the maximum value of y is y=4.5.