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\begin{array}{c}\phantom{\times}241567\\\underline{\times\phantom{}15678}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times}241567\\\underline{\times\phantom{}15678}\\\phantom{\times}1932536\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 241567 with 8. Write the result 1932536 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times}241567\\\underline{\times\phantom{}15678}\\\phantom{\times}1932536\\\phantom{\times}1690969\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 241567 with 7. Write the result 1690969 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times}241567\\\underline{\times\phantom{}15678}\\\phantom{\times}1932536\\\phantom{\times}1690969\phantom{9}\\\phantom{\times}1449402\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 241567 with 6. Write the result 1449402 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times}241567\\\underline{\times\phantom{}15678}\\\phantom{\times}1932536\\\phantom{\times}1690969\phantom{9}\\\phantom{\times}1449402\phantom{99}\\\phantom{\times}1207835\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 241567 with 5. Write the result 1207835 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times}241567\\\underline{\times\phantom{}15678}\\\phantom{\times}1932536\\\phantom{\times}1690969\phantom{9}\\\phantom{\times}1449402\phantom{99}\\\phantom{\times}1207835\phantom{999}\\\underline{\phantom{\times}241567\phantom{9999}}\\\end{array}
Now multiply the first number with the 5^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 241567 with 1. Write the result 241567 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times}241567\\\underline{\times\phantom{}15678}\\\phantom{\times}1932536\\\phantom{\times}1690969\phantom{9}\\\phantom{\times}1449402\phantom{99}\\\phantom{\times}1207835\phantom{999}\\\underline{\phantom{\times}241567\phantom{9999}}\\\phantom{\times}-507679870\end{array}
Now add the intermediate results to get final answer.