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\begin{array}{c}\phantom{\times999}21487\\\underline{\times\phantom{9999}2879}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times999}21487\\\underline{\times\phantom{9999}2879}\\\phantom{\times99}193383\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 21487 with 9. Write the result 193383 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times999}21487\\\underline{\times\phantom{9999}2879}\\\phantom{\times99}193383\\\phantom{\times9}150409\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 21487 with 7. Write the result 150409 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times999}21487\\\underline{\times\phantom{9999}2879}\\\phantom{\times99}193383\\\phantom{\times9}150409\phantom{9}\\\phantom{\times}171896\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 21487 with 8. Write the result 171896 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times999}21487\\\underline{\times\phantom{9999}2879}\\\phantom{\times99}193383\\\phantom{\times9}150409\phantom{9}\\\phantom{\times}171896\phantom{99}\\\underline{\phantom{\times}42974\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 21487 with 2. Write the result 42974 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times999}21487\\\underline{\times\phantom{9999}2879}\\\phantom{\times99}193383\\\phantom{\times9}150409\phantom{9}\\\phantom{\times}171896\phantom{99}\\\underline{\phantom{\times}42974\phantom{999}}\\\phantom{\times}61861073\end{array}
Now add the intermediate results to get final answer.