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\begin{array}{c}\phantom{\times9999}5869\\\underline{\times\phantom{9999}5869}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times9999}5869\\\underline{\times\phantom{9999}5869}\\\phantom{\times999}52821\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 5869 with 9. Write the result 52821 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}5869\\\underline{\times\phantom{9999}5869}\\\phantom{\times999}52821\\\phantom{\times99}35214\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 5869 with 6. Write the result 35214 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}5869\\\underline{\times\phantom{9999}5869}\\\phantom{\times999}52821\\\phantom{\times99}35214\phantom{9}\\\phantom{\times9}46952\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 5869 with 8. Write the result 46952 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}5869\\\underline{\times\phantom{9999}5869}\\\phantom{\times999}52821\\\phantom{\times99}35214\phantom{9}\\\phantom{\times9}46952\phantom{99}\\\underline{\phantom{\times}29345\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 5869 with 5. Write the result 29345 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}5869\\\underline{\times\phantom{9999}5869}\\\phantom{\times999}52821\\\phantom{\times99}35214\phantom{9}\\\phantom{\times9}46952\phantom{99}\\\underline{\phantom{\times}29345\phantom{999}}\\\phantom{\times}34445161\end{array}
Now add the intermediate results to get final answer.