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\begin{array}{c}\phantom{\times9999}14\\\underline{\times\phantom{9}21397}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times9999}14\\\underline{\times\phantom{9}21397}\\\phantom{\times9999}98\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 14 with 7. Write the result 98 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}14\\\underline{\times\phantom{9}21397}\\\phantom{\times9999}98\\\phantom{\times99}126\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 14 with 9. Write the result 126 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}14\\\underline{\times\phantom{9}21397}\\\phantom{\times9999}98\\\phantom{\times99}126\phantom{9}\\\phantom{\times99}42\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 14 with 3. Write the result 42 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}14\\\underline{\times\phantom{9}21397}\\\phantom{\times9999}98\\\phantom{\times99}126\phantom{9}\\\phantom{\times99}42\phantom{99}\\\phantom{\times9}14\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 14 with 1. Write the result 14 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}14\\\underline{\times\phantom{9}21397}\\\phantom{\times9999}98\\\phantom{\times99}126\phantom{9}\\\phantom{\times99}42\phantom{99}\\\phantom{\times9}14\phantom{999}\\\underline{\phantom{\times}28\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 14 with 2. Write the result 28 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}14\\\underline{\times\phantom{9}21397}\\\phantom{\times9999}98\\\phantom{\times99}126\phantom{9}\\\phantom{\times99}42\phantom{99}\\\phantom{\times9}14\phantom{999}\\\underline{\phantom{\times}28\phantom{9999}}\\\phantom{\times}299558\end{array}
Now add the intermediate results to get final answer.