1. **State the problem:** Simplify the expression $x(x - 1)(x + 4) - 2x^2 + 4$. 2. **Expand the product:** First, expand $x(x - 1)(x + 4)$. $$x(x - 1)(x + 4) = x[(x - 1)(x + 4)]$$ 3. **Multiply inside the brackets:** $$(x - 1)(x + 4) = x^2 + 4x - x - 4 = x^2 + 3x - 4$$ 4. **Multiply by $x$:** $$x(x^2 + 3x - 4) = x^3 + 3x^2 - 4x$$ 5. **Rewrite the original expression:** $$x^3 + 3x^2 - 4x - 2x^2 + 4$$ 6. **Combine like terms:** $$x^3 + (3x^2 - 2x^2) - 4x + 4 = x^3 + x^2 - 4x + 4$$ 7. **Final simplified expression:** $$\boxed{x^3 + x^2 - 4x + 4}$$