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The y-coordinate of F is 8.

Step-by-step explanation:

The area of the large triangle = 1/2 * base * height.

From the given coordinates:

The base of the large triangle =  x coordinate of C - x coordinate of A

= 11 - 3 = 8 units.

It's height = y coordinate of A = 12, so

Area of large triangle = 1/2 * 8 * 12 = 48 unit^2.

Using a similar calculation for the small triangle:

Base = 10 - 6 = 4 and height = k units.

So it's area = 1/2 * 4 * k = 2k unit^2.

So from given area of the shaded part:

48 - 2k = 32

-2k = -16

k = 8.