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\begin{array}{c}\phantom{\times99999}5444\\\underline{\times\phantom{999}100369}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times99999}5444\\\underline{\times\phantom{999}100369}\\\phantom{\times9999}48996\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 5444 with 9. Write the result 48996 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}5444\\\underline{\times\phantom{999}100369}\\\phantom{\times9999}48996\\\phantom{\times999}32664\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 5444 with 6. Write the result 32664 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}5444\\\underline{\times\phantom{999}100369}\\\phantom{\times9999}48996\\\phantom{\times999}32664\phantom{9}\\\phantom{\times99}16332\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 5444 with 3. Write the result 16332 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}5444\\\underline{\times\phantom{999}100369}\\\phantom{\times9999}48996\\\phantom{\times999}32664\phantom{9}\\\phantom{\times99}16332\phantom{99}\\\phantom{\times999999}0\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 5444 with 0. Write the result 0 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}5444\\\underline{\times\phantom{999}100369}\\\phantom{\times9999}48996\\\phantom{\times999}32664\phantom{9}\\\phantom{\times99}16332\phantom{99}\\\phantom{\times999999}0\phantom{999}\\\phantom{\times99999}0\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 5444 with 0. Write the result 0 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}5444\\\underline{\times\phantom{999}100369}\\\phantom{\times9999}48996\\\phantom{\times999}32664\phantom{9}\\\phantom{\times99}16332\phantom{99}\\\phantom{\times999999}0\phantom{999}\\\phantom{\times99999}0\phantom{9999}\\\underline{\phantom{\times}5444\phantom{99999}}\\\end{array}
Now multiply the first number with the 6^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 5444 with 1. Write the result 5444 at the end leaving 5 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}5444\\\underline{\times\phantom{999}100369}\\\phantom{\times9999}48996\\\phantom{\times999}32664\phantom{9}\\\phantom{\times99}16332\phantom{99}\\\phantom{\times999999}0\phantom{999}\\\phantom{\times99999}0\phantom{9999}\\\underline{\phantom{\times}5444\phantom{99999}}\\\phantom{\times}546408836\end{array}
Now add the intermediate results to get final answer.