Expanding the left side of the inequality, we get:

(y+4)(4-y) + (y+5)y

= 4y - y^2 + 16 - 4y + y^2 + 5y

= 5y + 16 + 5y

= 10y + 16

Now, the inequality becomes:

10y + 16 > 6y - 20

Subtracting 6y from both sides, we get:

4y + 16 > -20

Subtracting 16 from both sides, we get:

4y > -36

Dividing by 4 on both sides, we get:

y > -9

Therefore, the solution for the inequality is y > -9.