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\begin{array}{c}\phantom{\times99}15899\\\underline{\times\phantom{9999}144}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times99}15899\\\underline{\times\phantom{9999}144}\\\phantom{\times99}63596\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 15899 with 4. Write the result 63596 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times99}15899\\\underline{\times\phantom{9999}144}\\\phantom{\times99}63596\\\phantom{\times9}63596\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 15899 with 4. Write the result 63596 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times99}15899\\\underline{\times\phantom{9999}144}\\\phantom{\times99}63596\\\phantom{\times9}63596\phantom{9}\\\underline{\phantom{\times}15899\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 15899 with 1. Write the result 15899 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times99}15899\\\underline{\times\phantom{9999}144}\\\phantom{\times99}63596\\\phantom{\times9}63596\phantom{9}\\\underline{\phantom{\times}15899\phantom{99}}\\\phantom{\times}2289456\end{array}
Now add the intermediate results to get final answer.