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\begin{array}{c}\phantom{\times99999}5869\\\underline{\times\phantom{9999}23652}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times99999}5869\\\underline{\times\phantom{9999}23652}\\\phantom{\times9999}11738\\\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 2. Write the result 11738 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}5869\\\underline{\times\phantom{9999}23652}\\\phantom{\times9999}11738\\\phantom{\times999}29345\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 5. Write the result 29345 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}5869\\\underline{\times\phantom{9999}23652}\\\phantom{\times9999}11738\\\phantom{\times999}29345\phantom{9}\\\phantom{\times99}35214\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 6. Write the result 35214 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}5869\\\underline{\times\phantom{9999}23652}\\\phantom{\times9999}11738\\\phantom{\times999}29345\phantom{9}\\\phantom{\times99}35214\phantom{99}\\\phantom{\times9}17607\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 3. Write the result 17607 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}5869\\\underline{\times\phantom{9999}23652}\\\phantom{\times9999}11738\\\phantom{\times999}29345\phantom{9}\\\phantom{\times99}35214\phantom{99}\\\phantom{\times9}17607\phantom{999}\\\underline{\phantom{\times}11738\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 5869 with 2. Write the result 11738 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times99999}5869\\\underline{\times\phantom{9999}23652}\\\phantom{\times9999}11738\\\phantom{\times999}29345\phantom{9}\\\phantom{\times99}35214\phantom{99}\\\phantom{\times9}17607\phantom{999}\\\underline{\phantom{\times}11738\phantom{9999}}\\\phantom{\times}138813588\end{array}
Now add the intermediate results to get final answer.