$2 i \frac{6 - 4 i}{3 + 3 i} = \frac{10 + 2 i}{3}$

Explanation

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$2 i \frac{6 - 4 i}{3 + 3 i} \overset{◯}{1} 2 i \frac{1 - 5 i}{3} \overset{◯}{2} \frac{- 10 i ^{2} + 2 i}{3} \overset{◯}{3} \frac{10 + 2 i}{3}$
①	Divide $6 - 4 i$ by $3 + 3 i$ to get $\frac{1 - 5 i}{3}$ . ( view steps )
②	Multiply $2 i$ by $\frac{1 - 5 i}{3}$ to get $\frac{- 10 i ^{2} + 2 i}{3}$ . Step 1: Write $2 i$ as a fraction by putting $1$ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $2 i \cdot \frac{1 - 5 i}{3} Step 1 \frac{2 i}{1} \cdot \frac{1 - 5 i}{3} Step 2 \frac{2 i \cdot ( 1 - 5 i )}{1 \cdot 3} = Step 3 \frac{2 i - 10 i ^{2}}{3} = \frac{- 10 i ^{2} + 2 i}{3}$
③	$- 10 i^{2} = - 10 \cdot (- 1) = 10$

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$2 i \frac{6 - 4 i}{3 + 3 i} = \frac{10 + 2 i}{3}$