To multiply the polynomial expressions \((x + 2)(x - 4)\), you can use the distributive property (also known as the FOIL method for binomials).
\[ (x + 2)(x - 4) = x \cdot x + x \cdot (-4) + 2 \cdot x + 2 \cdot (-4) \]
Now, let's calculate each term:
- \(x \cdot x = x^2\)
- \(x \cdot (-4) = -4x\)
- \(2 \cdot x = 2x\)
- \(2 \cdot (-4) = -8\)
Now, combine all the terms:
\[ x^2 - 4x + 2x - 8 \]
Combine the like terms \(-4x\) and \(2x\):
\[ x^2 - 2x - 8 \]
So, the result of the multiplication is:
\[ \boxed{x^2 - 2x - 8} \]