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\begin{array}{c}\phantom{\times99}6543210\\\underline{\times\phantom{999}123456}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times99}6543210\\\underline{\times\phantom{999}123456}\\\phantom{\times9}39259260\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 6543210 with 6. Write the result 39259260 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times99}6543210\\\underline{\times\phantom{999}123456}\\\phantom{\times9}39259260\\\phantom{\times}32716050\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 6543210 with 5. Write the result 32716050 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times99}6543210\\\underline{\times\phantom{999}123456}\\\phantom{\times9}39259260\\\phantom{\times}32716050\phantom{9}\\\phantom{\times}26172840\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 6543210 with 4. Write the result 26172840 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times99}6543210\\\underline{\times\phantom{999}123456}\\\phantom{\times9}39259260\\\phantom{\times}32716050\phantom{9}\\\phantom{\times}26172840\phantom{99}\\\phantom{\times}19629630\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 6543210 with 3. Write the result 19629630 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times99}6543210\\\underline{\times\phantom{999}123456}\\\phantom{\times9}39259260\\\phantom{\times}32716050\phantom{9}\\\phantom{\times}26172840\phantom{99}\\\phantom{\times}19629630\phantom{999}\\\phantom{\times}13086420\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 6543210 with 2. Write the result 13086420 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times99}6543210\\\underline{\times\phantom{999}123456}\\\phantom{\times9}39259260\\\phantom{\times}32716050\phantom{9}\\\phantom{\times}26172840\phantom{99}\\\phantom{\times}19629630\phantom{999}\\\phantom{\times}13086420\phantom{9999}\\\underline{\phantom{\times}6543210\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 6543210 with 1. Write the result 6543210 at the end leaving 5 spaces to the right like this.
\begin{array}{c}\phantom{\times99}6543210\\\underline{\times\phantom{999}123456}\\\phantom{\times9}39259260\\\phantom{\times}32716050\phantom{9}\\\phantom{\times}26172840\phantom{99}\\\phantom{\times}19629630\phantom{999}\\\phantom{\times}13086420\phantom{9999}\\\underline{\phantom{\times}6543210\phantom{99999}}\\\phantom{\times}344682112\end{array}
Now add the intermediate results to get final answer.