Given f(x) = ax^3 + bx^2 + cx + d:
f(4) = 64a + 16b+4c+d

f(-2) = -8a + 4b - 2c + d = 3


At a maximum or minimum (for a polynomial), the derivative equals 0 (horizontal tangent).
Since f '(x) = 3ax^2 + 2bx + c
f '(4) = 48a + 8b + c = 0.

f '(-2) = 12a - 4b + c = 0

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Now, we have 4 equations in 4 unknowns
-8a + 4b - 2c + d =-10
64a + 16b + 4c + d = 0
12a - 4b + c = 0
48a + 8b + c = 0.