Answer
$1580_{nine}$
Work Step by Step
$(6\times 3)_{10}=(18)_{10}=2\times 9+0=(20)_{9}$
Record the $0$; carry the $2$.
$\begin{array}{llll}
& 2 & 4 & 3_{nine}\\
\times & & & 6_{nine}\\
-- & -- & -- & --\\
& & & 0_{nine}
\end{array}$
$(6\times 4+2)_{10}=(26)_{10}=2\times 9+8=(28)_{9}$
Record the $8$; carry the $2$.
$\begin{array}{llll}
& 2 & 4 & 3_{nine}\\
\times & & & 6_{nine}\\
-- & -- & -- & --\\
& & 8 & 0_{nine}
\end{array}$
$(6\times 2+2)_{10}=(14)_{10}=1\times 9+5=(15)_{9}$
Record the $15.$
Result: $1580_{nine}$