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\begin{array}{c}\phantom{\times999}1723\\\underline{\times\phantom{999}1678}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times999}1723\\\underline{\times\phantom{999}1678}\\\phantom{\times99}13784\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 1723 with 8. Write the result 13784 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times999}1723\\\underline{\times\phantom{999}1678}\\\phantom{\times99}13784\\\phantom{\times9}12061\phantom{9}\\\end{array}
Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 1723 with 7. Write the result 12061 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times999}1723\\\underline{\times\phantom{999}1678}\\\phantom{\times99}13784\\\phantom{\times9}12061\phantom{9}\\\phantom{\times}10338\phantom{99}\\\end{array}
Now multiply the first number with the 3^{rd} digit in 2^{nd} number to get intermediate results. That is Multiply 1723 with 6. Write the result 10338 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times999}1723\\\underline{\times\phantom{999}1678}\\\phantom{\times99}13784\\\phantom{\times9}12061\phantom{9}\\\phantom{\times}10338\phantom{99}\\\underline{\phantom{\times}1723\phantom{999}}\\\end{array}
Now multiply the first number with the 4^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 1723 with 1. Write the result 1723 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times999}1723\\\underline{\times\phantom{999}1678}\\\phantom{\times99}13784\\\phantom{\times9}12061\phantom{9}\\\phantom{\times}10338\phantom{99}\\\underline{\phantom{\times}1723\phantom{999}}\\\phantom{\times}2891194\end{array}
Now add the intermediate results to get final answer.