1. Stating the problem: Simplify the algebraic expression $$\frac{x^2(x+2)(x-4)}{6x(x^2+x-20)}.$$\n\n2. Factor the quadratic in the denominator: \n$$x^2+x-20 = (x+5)(x-4).$$\n\n3. Rewrite the expression with factored form: \n$$\frac{x^2(x+2)(x-4)}{6x(x+5)(x-4)}.$$\n\n4. Cancel common factors: both numerator and denominator have an \(x-4\) term, and both have an \(x\) (since numerator has \(x^2\) and denominator has \(x\)).\n\nAfter cancellation:\n$$\frac{x(x+2)}{6(x+5)}.$$\n\n5. Final simplified expression: $$\boxed{\frac{x(x+2)}{6(x+5)}}.$$