Simplify -2i*(2+6i)

$- 2 i \cdot (2 + 6 i)$

Apply the distributive property.

$- 2 i \cdot 2 - 2 i (6 i)$

Multiply $2$ by $- 2$ .

$- 4 i - 2 i (6 i)$

Multiply $- 2 i (6 i)$ .

Multiply $6$ by $- 2$ .

$- 4 i - 12 i i$

Raise $i$ to the power of $1$ .

$- 4 i - 12 (i^{1} i)$

Raise $i$ to the power of $1$ .

$- 4 i - 12 (i^{1} i^{1})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 4 i - 12 i^{1 + 1}$

Add $1$ and $1$ .

$- 4 i - 12 i^{2}$

Simplify each term.

Rewrite $i^{2}$ as $- 1$ .

$- 4 i - 12 \cdot - 1$

Multiply $- 12$ by $- 1$ .

$- 4 i + 12$

Reorder $- 4 i$ and $12$ .

$12 - 4 i$