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\begin{array}{c}\phantom{\times99}6000000\\\underline{\times\phantom{99}5000123}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times99}6000000\\\underline{\times\phantom{99}5000123}\\\phantom{\times9}18000000\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 6000000 with 3. Write the result 18000000 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times99}6000000\\\underline{\times\phantom{99}5000123}\\\phantom{\times9}18000000\\\phantom{\times}12000000\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 6000000 with 2. Write the result 12000000 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times99}6000000\\\underline{\times\phantom{99}5000123}\\\phantom{\times9}18000000\\\phantom{\times}12000000\phantom{9}\\\phantom{\times}6000000\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 6000000 with 1. Write the result 6000000 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times99}6000000\\\underline{\times\phantom{99}5000123}\\\phantom{\times9}18000000\\\phantom{\times}12000000\phantom{9}\\\phantom{\times}6000000\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 6000000 with 0. Write the result 0 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times99}6000000\\\underline{\times\phantom{99}5000123}\\\phantom{\times9}18000000\\\phantom{\times}12000000\phantom{9}\\\phantom{\times}6000000\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 6000000 with 0. Write the result 0 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times99}6000000\\\underline{\times\phantom{99}5000123}\\\phantom{\times9}18000000\\\phantom{\times}12000000\phantom{9}\\\phantom{\times}6000000\phantom{99}\\\phantom{\times999999}0\phantom{999}\\\phantom{\times99999}0\phantom{9999}\\\phantom{\times9999}0\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 6000000 with 0. Write the result 0 at the end leaving 5 spaces to the right like this.
\begin{array}{c}\phantom{\times99}6000000\\\underline{\times\phantom{99}5000123}\\\phantom{\times9}18000000\\\phantom{\times}12000000\phantom{9}\\\phantom{\times}6000000\phantom{99}\\\phantom{\times999999}0\phantom{999}\\\phantom{\times99999}0\phantom{9999}\\\phantom{\times9999}0\phantom{99999}\\\underline{\phantom{\times}30000000\phantom{999999}}\\\end{array}
Now multiply the first number with the 7^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 6000000 with 5. Write the result 30000000 at the end leaving 6 spaces to the right like this.
\begin{array}{c}\phantom{\times99}6000000\\\underline{\times\phantom{99}5000123}\\\phantom{\times9}18000000\\\phantom{\times}12000000\phantom{9}\\\phantom{\times}6000000\phantom{99}\\\phantom{\times999999}0\phantom{999}\\\phantom{\times99999}0\phantom{9999}\\\phantom{\times9999}0\phantom{99999}\\\underline{\phantom{\times}30000000\phantom{999999}}\\\phantom{\times}391437440\end{array}
Now add the intermediate results to get final answer.