Solution f2a45a50-cc78-42af-bd35-71355caa4b64

Points: 1 pt

We split each factor by place value:
\[
(345)_6=(300)_6+(40)_6+(5)_6,
\]
\[
(214)_6=(200)_6+(10)_6+(4)_6.
\]

Using a multiplication table,

$\times$ | $(300)_6$ | $(40)_6$ | $(5)_6$ 

$(200)_6$ | $(100000)_6$ | $(12000)_6$ | $(1400)_6$ 

$(10)_6$ | $(3000)_6$ | $(400)_6$ | $(50)_6$ 

$(4)_6$ | $(2000)_6$ | $(240)_6$ | $(32)_6$ 

Adding all of the entries,
\[
\begin{aligned}
&(100000+12000+1400+3000+400+50+2000+240+32)_6\\
&\qquad=(124002)_6.
\end{aligned}
\]

Final answer:
(124002)_6