#### Answer

$6-6i$

#### Work Step by Step

$(8-\sqrt {-4})-(2+\sqrt {-16})$
=$(8-\sqrt {-1\times4})-(2+\sqrt {-1\times16})$
=$(8-\sqrt {-1}\sqrt 4)-(2+\sqrt {-1}\sqrt {16})$
=$(8-i\sqrt 4)-(2+i\sqrt {16})$
=$(8-2i)-(2+4i)$
=$8-2i-2-4i$
=$8-2-2i-4i$
=$6-6i$