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\begin{array}{c}\phantom{\times9999}56298\\\underline{\times\phantom{99}7862354}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times9999}56298\\\underline{\times\phantom{99}7862354}\\\phantom{\times999}225192\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 56298 with 4. Write the result 225192 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}56298\\\underline{\times\phantom{99}7862354}\\\phantom{\times999}225192\\\phantom{\times99}281490\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 56298 with 5. Write the result 281490 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}56298\\\underline{\times\phantom{99}7862354}\\\phantom{\times999}225192\\\phantom{\times99}281490\phantom{9}\\\phantom{\times9}168894\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 56298 with 3. Write the result 168894 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}56298\\\underline{\times\phantom{99}7862354}\\\phantom{\times999}225192\\\phantom{\times99}281490\phantom{9}\\\phantom{\times9}168894\phantom{99}\\\phantom{\times}112596\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 56298 with 2. Write the result 112596 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}56298\\\underline{\times\phantom{99}7862354}\\\phantom{\times999}225192\\\phantom{\times99}281490\phantom{9}\\\phantom{\times9}168894\phantom{99}\\\phantom{\times}112596\phantom{999}\\\phantom{\times}337788\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 56298 with 6. Write the result 337788 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}56298\\\underline{\times\phantom{99}7862354}\\\phantom{\times999}225192\\\phantom{\times99}281490\phantom{9}\\\phantom{\times9}168894\phantom{99}\\\phantom{\times}112596\phantom{999}\\\phantom{\times}337788\phantom{9999}\\\phantom{\times}450384\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 56298 with 8. Write the result 450384 at the end leaving 5 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}56298\\\underline{\times\phantom{99}7862354}\\\phantom{\times999}225192\\\phantom{\times99}281490\phantom{9}\\\phantom{\times9}168894\phantom{99}\\\phantom{\times}112596\phantom{999}\\\phantom{\times}337788\phantom{9999}\\\phantom{\times}450384\phantom{99999}\\\underline{\phantom{\times}394086\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 56298 with 7. Write the result 394086 at the end leaving 6 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}56298\\\underline{\times\phantom{99}7862354}\\\phantom{\times999}225192\\\phantom{\times99}281490\phantom{9}\\\phantom{\times9}168894\phantom{99}\\\phantom{\times}112596\phantom{999}\\\phantom{\times}337788\phantom{9999}\\\phantom{\times}450384\phantom{99999}\\\underline{\phantom{\times}394086\phantom{999999}}\\\phantom{\times}253174004\end{array}
Now add the intermediate results to get final answer.