Multiply each term of $ \left( \color{blue}{x+1}\right) $ by each term in $ \left( x-4\right) $.

$$ \left( \color{blue}{x+1}\right) \cdot \left( x-4\right) = x^2-4x+x-4 $$

Combine like terms:

$$ x^2 \color{blue}{-4x} + \color{blue}{x} -4 = x^2 \color{blue}{-3x} -4 $$

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

$$ \left( \color{blue}{x^2-3x-4}\right) \cdot \left( x-4-2i\right) = x^3-4x^2-2ix^2-3x^2+12x+6ix-4x+16+8i $$

Combine like terms:

$$ x^3 \color{blue}{-4x^2} -2ix^2 \color{blue}{-3x^2} + \color{red}{12x} +6ix \color{red}{-4x} +16+8i = -2ix^2+x^3+6ix \color{blue}{-7x^2} +8i+ \color{red}{8x} +16 $$

Multiply each term of $ \left( \color{blue}{-2ix^2+x^3+6ix-7x^2+8i+8x+16}\right) $ by each term in $ \left( x-4+2i\right) $.

$$ \left( \color{blue}{-2ix^2+x^3+6ix-7x^2+8i+8x+16}\right) \cdot \left( x-4+2i\right) = \\ = -\cancel{2ix^3}+8ix^2-4i^2x^2+x^4-4x^3+ \cancel{2ix^3}+6ix^2-24ix+12i^2x-7x^3+28x^2-14ix^2+8ix -\cancel{32i}+16i^2+8x^2-32x+16ix+16x-64+ \cancel{32i} $$

Combine like terms:

$$ \, \color{blue}{ -\cancel{2ix^3}} \,+ \color{green}{8ix^2} -4i^2x^2+x^4 \color{orange}{-4x^3} + \, \color{blue}{ \cancel{2ix^3}} \,+ \color{blue}{6ix^2} \color{red}{-24ix} +12i^2x \color{orange}{-7x^3} + \color{green}{28x^2} \color{blue}{-14ix^2} + \color{orange}{8ix} \, \color{blue}{ -\cancel{32i}} \,+16i^2+ \color{green}{8x^2} \color{green}{-32x} + \color{orange}{16ix} + \color{green}{16x} -64+ \, \color{blue}{ \cancel{32i}} \, = \\ = -4i^2x^2+x^4+12i^2x \color{orange}{-11x^3} +16i^2+ \color{green}{36x^2} \color{green}{-16x} -64 $$