Answer
$$6i$$
Work Step by Step
$$\eqalign{
& \left( {\sqrt 6 \operatorname{cis} {{120}^ \circ }} \right)\left( {\sqrt 6 \operatorname{cis} \left( { - {{30}^ \circ }} \right)} \right) \cr
& {\text{Multiply using the Product Theorem}} \cr
& = \left( {\sqrt 6 } \right)\left( {\sqrt 6 } \right)\operatorname{cis} \left( {{{120}^ \circ } - {{30}^ \circ }} \right) \cr
& {\text{Simplify}} \cr
& = 6\operatorname{cis} \left( {{{90}^ \circ }} \right) \cr
& = 6\left( {\cos {{90}^ \circ } + i\sin {{90}^ \circ }} \right) \cr
& {\text{Write in Rectangular form}} \cr
& = 6\left( {{0^ \circ } + i\left( 1 \right)} \right) \cr
& = 6i \cr} $$
