Thinking Mathematically (6th Edition)

$123_{four}$
$(3\times 1)_{10}=(3)_{10}=(3)_{4}$ Record the $3$; there is nothing to carry. $\begin{array}{llll} & 2 & 1_{four} & \\ \times & & 3_{four} & \\ -- & -- & -- & \\ & & 3_{four} & \end{array}$ $(3\times 2)_{10}=(6)_{10}=1\times 4+2=(12)_{4}$ Record the $12.$ Result: $123_{four}$