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\begin{array}{c}\phantom{\times}113150\\\underline{\times\phantom{}144376}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times}113150\\\underline{\times\phantom{}144376}\\\phantom{\times}678900\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 113150 with 6. Write the result 678900 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times}113150\\\underline{\times\phantom{}144376}\\\phantom{\times}678900\\\phantom{\times}792050\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 113150 with 7. Write the result 792050 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times}113150\\\underline{\times\phantom{}144376}\\\phantom{\times}678900\\\phantom{\times}792050\phantom{9}\\\phantom{\times}339450\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 113150 with 3. Write the result 339450 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times}113150\\\underline{\times\phantom{}144376}\\\phantom{\times}678900\\\phantom{\times}792050\phantom{9}\\\phantom{\times}339450\phantom{99}\\\phantom{\times}452600\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 113150 with 4. Write the result 452600 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times}113150\\\underline{\times\phantom{}144376}\\\phantom{\times}678900\\\phantom{\times}792050\phantom{9}\\\phantom{\times}339450\phantom{99}\\\phantom{\times}452600\phantom{999}\\\phantom{\times}452600\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 113150 with 4. Write the result 452600 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times}113150\\\underline{\times\phantom{}144376}\\\phantom{\times}678900\\\phantom{\times}792050\phantom{9}\\\phantom{\times}339450\phantom{99}\\\phantom{\times}452600\phantom{999}\\\phantom{\times}452600\phantom{9999}\\\underline{\phantom{\times}113150\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 113150 with 1. Write the result 113150 at the end leaving 5 spaces to the right like this.
\begin{array}{c}\phantom{\times}113150\\\underline{\times\phantom{}144376}\\\phantom{\times}678900\\\phantom{\times}792050\phantom{9}\\\phantom{\times}339450\phantom{99}\\\phantom{\times}452600\phantom{999}\\\phantom{\times}452600\phantom{9999}\\\underline{\phantom{\times}113150\phantom{99999}}\\\phantom{\times}-843724784\end{array}
Now add the intermediate results to get final answer.