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\begin{array}{c}\phantom{\times999}19537\\\underline{\times\phantom{9999}1147}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times999}19537\\\underline{\times\phantom{9999}1147}\\\phantom{\times99}136759\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 19537 with 7. Write the result 136759 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times999}19537\\\underline{\times\phantom{9999}1147}\\\phantom{\times99}136759\\\phantom{\times99}78148\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 19537 with 4. Write the result 78148 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times999}19537\\\underline{\times\phantom{9999}1147}\\\phantom{\times99}136759\\\phantom{\times99}78148\phantom{9}\\\phantom{\times9}19537\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 19537 with 1. Write the result 19537 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times999}19537\\\underline{\times\phantom{9999}1147}\\\phantom{\times99}136759\\\phantom{\times99}78148\phantom{9}\\\phantom{\times9}19537\phantom{99}\\\underline{\phantom{\times}19537\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 19537 with 1. Write the result 19537 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times999}19537\\\underline{\times\phantom{9999}1147}\\\phantom{\times99}136759\\\phantom{\times99}78148\phantom{9}\\\phantom{\times9}19537\phantom{99}\\\underline{\phantom{\times}19537\phantom{999}}\\\phantom{\times}22408939\end{array}
Now add the intermediate results to get final answer.