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\begin{array}{c}\phantom{\times}6358\\\underline{\times\phantom{}635821}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times}6358\\\underline{\times\phantom{}635821}\\\phantom{\times}6358\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 6358 with 1. Write the result 6358 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times}6358\\\underline{\times\phantom{}635821}\\\phantom{\times}6358\\\phantom{\times}12716\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 6358 with 2. Write the result 12716 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times}6358\\\underline{\times\phantom{}635821}\\\phantom{\times}6358\\\phantom{\times}12716\phantom{9}\\\phantom{\times}50864\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 6358 with 8. Write the result 50864 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times}6358\\\underline{\times\phantom{}635821}\\\phantom{\times}6358\\\phantom{\times}12716\phantom{9}\\\phantom{\times}50864\phantom{99}\\\phantom{\times}31790\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 6358 with 5. Write the result 31790 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times}6358\\\underline{\times\phantom{}635821}\\\phantom{\times}6358\\\phantom{\times}12716\phantom{9}\\\phantom{\times}50864\phantom{99}\\\phantom{\times}31790\phantom{999}\\\phantom{\times}19074\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 6358 with 3. Write the result 19074 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times}6358\\\underline{\times\phantom{}635821}\\\phantom{\times}6358\\\phantom{\times}12716\phantom{9}\\\phantom{\times}50864\phantom{99}\\\phantom{\times}31790\phantom{999}\\\phantom{\times}19074\phantom{9999}\\\underline{\phantom{\times}38148\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 6358 with 6. Write the result 38148 at the end leaving 5 spaces to the right like this.
\begin{array}{c}\phantom{\times}6358\\\underline{\times\phantom{}635821}\\\phantom{\times}6358\\\phantom{\times}12716\phantom{9}\\\phantom{\times}50864\phantom{99}\\\phantom{\times}31790\phantom{999}\\\phantom{\times}19074\phantom{9999}\\\underline{\phantom{\times}38148\phantom{99999}}\\\phantom{\times}-252417378\end{array}
Now add the intermediate results to get final answer.