Multiply each term of $ \left( \color{blue}{x+2}\right) $ by each term in $ \left( x+4\right) $.

$$ \left( \color{blue}{x+2}\right) \cdot \left( x+4\right) = x^2+4x+2x+8 $$

Combine like terms:

$$ x^2+ \color{blue}{4x} + \color{blue}{2x} +8 = x^2+ \color{blue}{6x} +8 $$

Multiply each term of $ \left( \color{blue}{x^2+6x+8}\right) $ by each term in $ \left( x-2\right) $.

$$ \left( \color{blue}{x^2+6x+8}\right) \cdot \left( x-2\right) = x^3-2x^2+6x^2-12x+8x-16 $$

Combine like terms:

$$ x^3 \color{blue}{-2x^2} + \color{blue}{6x^2} \color{red}{-12x} + \color{red}{8x} -16 = x^3+ \color{blue}{4x^2} \color{red}{-4x} -16 $$

Multiply each term of $ \left( \color{blue}{x^3+4x^2-4x-16}\right) $ by each term in $ \left( x-4\right) $.

$$ \left( \color{blue}{x^3+4x^2-4x-16}\right) \cdot \left( x-4\right) = \\ = x^4 -\cancel{4x^3}+ \cancel{4x^3}-16x^2-4x^2+ \cancel{16x} -\cancel{16x}+64 $$

Combine like terms:

$$ x^4 \, \color{blue}{ -\cancel{4x^3}} \,+ \, \color{blue}{ \cancel{4x^3}} \, \color{green}{-16x^2} \color{green}{-4x^2} + \, \color{orange}{ \cancel{16x}} \, \, \color{orange}{ -\cancel{16x}} \,+64 = x^4 \color{green}{-20x^2} +64 $$