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\begin{array}{c}\phantom{\times}42682\\\underline{\times\phantom{}586238692}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times}42682\\\underline{\times\phantom{}586238692}\\\phantom{\times}85364\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 42682 with 2. Write the result 85364 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times}42682\\\underline{\times\phantom{}586238692}\\\phantom{\times}85364\\\phantom{\times}384138\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 42682 with 9. Write the result 384138 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times}42682\\\underline{\times\phantom{}586238692}\\\phantom{\times}85364\\\phantom{\times}384138\phantom{9}\\\phantom{\times}256092\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 42682 with 6. Write the result 256092 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times}42682\\\underline{\times\phantom{}586238692}\\\phantom{\times}85364\\\phantom{\times}384138\phantom{9}\\\phantom{\times}256092\phantom{99}\\\phantom{\times}341456\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 42682 with 8. Write the result 341456 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times}42682\\\underline{\times\phantom{}586238692}\\\phantom{\times}85364\\\phantom{\times}384138\phantom{9}\\\phantom{\times}256092\phantom{99}\\\phantom{\times}341456\phantom{999}\\\phantom{\times}128046\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 42682 with 3. Write the result 128046 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times}42682\\\underline{\times\phantom{}586238692}\\\phantom{\times}85364\\\phantom{\times}384138\phantom{9}\\\phantom{\times}256092\phantom{99}\\\phantom{\times}341456\phantom{999}\\\phantom{\times}128046\phantom{9999}\\\phantom{\times}85364\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 42682 with 2. Write the result 85364 at the end leaving 5 spaces to the right like this.
\begin{array}{c}\phantom{\times}42682\\\underline{\times\phantom{}586238692}\\\phantom{\times}85364\\\phantom{\times}384138\phantom{9}\\\phantom{\times}256092\phantom{99}\\\phantom{\times}341456\phantom{999}\\\phantom{\times}128046\phantom{9999}\\\phantom{\times}85364\phantom{99999}\\\phantom{\times}256092\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 42682 with 6. Write the result 256092 at the end leaving 6 spaces to the right like this.
\begin{array}{c}\phantom{\times}42682\\\underline{\times\phantom{}586238692}\\\phantom{\times}85364\\\phantom{\times}384138\phantom{9}\\\phantom{\times}256092\phantom{99}\\\phantom{\times}341456\phantom{999}\\\phantom{\times}128046\phantom{9999}\\\phantom{\times}85364\phantom{99999}\\\phantom{\times}256092\phantom{999999}\\\phantom{\times}341456\phantom{9999999}\\\end{array}
Now multiply the first number with the 8^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 42682 with 8. Write the result 341456 at the end leaving 7 spaces to the right like this.
\begin{array}{c}\phantom{\times}42682\\\underline{\times\phantom{}586238692}\\\phantom{\times}85364\\\phantom{\times}384138\phantom{9}\\\phantom{\times}256092\phantom{99}\\\phantom{\times}341456\phantom{999}\\\phantom{\times}128046\phantom{9999}\\\phantom{\times}85364\phantom{99999}\\\phantom{\times}256092\phantom{999999}\\\phantom{\times}341456\phantom{9999999}\\\underline{\phantom{\times}213410\phantom{99999999}}\\\end{array}
Now multiply the first number with the 9^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 42682 with 5. Write the result 213410 at the end leaving 8 spaces to the right like this.
\begin{array}{c}\phantom{\times}42682\\\underline{\times\phantom{}586238692}\\\phantom{\times}85364\\\phantom{\times}384138\phantom{9}\\\phantom{\times}256092\phantom{99}\\\phantom{\times}341456\phantom{999}\\\phantom{\times}128046\phantom{9999}\\\phantom{\times}85364\phantom{99999}\\\phantom{\times}256092\phantom{999999}\\\phantom{\times}341456\phantom{9999999}\\\underline{\phantom{\times}213410\phantom{99999999}}\\\phantom{\times}-639614552\end{array}
Now add the intermediate results to get final answer.