$$ (3n-x)^4 = (3n-x)^2 \cdot (3n-x)^2 $$

Find $ \left(3n-x\right)^2 $ using formula.

$$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$

where $ A = \color{blue}{ 3n } $ and $ B = \color{red}{ x }$.

$$ \begin{aligned}\left(3n-x\right)^2 = \color{blue}{\left( 3n \right)^2} -2 \cdot 3n \cdot x + \color{red}{x^2} = 9n^2-6nx+x^2\end{aligned} $$

Multiply each term of $ \left( \color{blue}{9n^2-6nx+x^2}\right) $ by each term in $ \left( 9n^2-6nx+x^2\right) $.

$$ \left( \color{blue}{9n^2-6nx+x^2}\right) \cdot \left( 9n^2-6nx+x^2\right) = \\ = 81n^4-54n^3x+9n^2x^2-54n^3x+36n^2x^2-6nx^3+9n^2x^2-6nx^3+x^4 $$

Combine like terms:

$$ 81n^4 \color{blue}{-54n^3x} + \color{red}{9n^2x^2} \color{blue}{-54n^3x} + \color{green}{36n^2x^2} \color{orange}{-6nx^3} + \color{green}{9n^2x^2} \color{orange}{-6nx^3} +x^4 = \\ = 81n^4 \color{blue}{-108n^3x} + \color{green}{54n^2x^2} \color{orange}{-12nx^3} +x^4 $$

Multiply each term of $ \left( \color{blue}{3n-x}\right) $ by each term in $ \left( 81n^4-108n^3x+54n^2x^2-12nx^3+x^4\right) $.

$$ \left( \color{blue}{3n-x}\right) \cdot \left( 81n^4-108n^3x+54n^2x^2-12nx^3+x^4\right) = \\ = 243n^5-324n^4x+162n^3x^2-36n^2x^3+3nx^4-81n^4x+108n^3x^2-54n^2x^3+12nx^4-x^5 $$

Combine like terms:

$$ 243n^5 \color{blue}{-324n^4x} + \color{red}{162n^3x^2} \color{green}{-36n^2x^3} + \color{orange}{3nx^4} \color{blue}{-81n^4x} + \color{red}{108n^3x^2} \color{green}{-54n^2x^3} + \color{orange}{12nx^4} -x^5 = \\ = 243n^5 \color{blue}{-405n^4x} + \color{red}{270n^3x^2} \color{green}{-90n^2x^3} + \color{orange}{15nx^4} -x^5 $$