If y(x) is the solution of the differential equation (x+2)dy/dx = x² + 4x, x ≠ -2 and y(0) = 0, then y(-4) is equal to:

We are given the differential equation (x+2)dy/dx = x² + 4x, with the condition y(0) = 0. We can rewrite the equation as:
dy/dx = (x² + 4x) / (x + 2)

We can factor the numerator:
dy/dx = x(x + 4) / (x + 2)

This is a separable differential equation. We can separate the variables and integrate:
dy = [x(x + 4) / (x + 2)] dx

To integrate the right-hand side, we perform polynomial long division:
x(x + 4) / (x + 2) = x + 2 - 4/(x + 2)

Therefore, the equation becomes:
dy = (x + 2 - 4/(x + 2)) dx

Integrating both sides:
∫dy = ∫(x + 2 - 4/(x + 2)) dx
y = (x²/2) + 2x - 4ln|x + 2| + C

We are given that y(0) = 0. Substituting this into the equation:
0 = (0²/2) + 2(0) - 4ln|0 + 2| + C
0 = -4ln(2) + C
C = 4ln(2)

So the solution is:
y = (x²/2) + 2x - 4ln|x + 2| + 4ln(2)
y = (x²/2) + 2x - 4ln|(x + 2)/2|

Now we need to find y(-4):
y(-4) = ((-4)²/2) + 2(-4) - 4ln|(-4 + 2)/2|
y(-4) = 8 - 8 - 4ln|-1|
y(-4) = -4ln(1)
y(-4) = 0

Therefore, y(-4) = 0