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\begin{array}{c}\phantom{\times9}123123113\\\underline{\times\phantom{99999}11317}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times9}123123113\\\underline{\times\phantom{99999}11317}\\\phantom{\times9}861861791\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 123123113 with 7. Write the result 861861791 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times9}123123113\\\underline{\times\phantom{99999}11317}\\\phantom{\times9}861861791\\\phantom{\times}123123113\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 123123113 with 1. Write the result 123123113 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times9}123123113\\\underline{\times\phantom{99999}11317}\\\phantom{\times9}861861791\\\phantom{\times}123123113\phantom{9}\\\phantom{\times}369369339\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 123123113 with 3. Write the result 369369339 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times9}123123113\\\underline{\times\phantom{99999}11317}\\\phantom{\times9}861861791\\\phantom{\times}123123113\phantom{9}\\\phantom{\times}369369339\phantom{99}\\\phantom{\times}123123113\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 123123113 with 1. Write the result 123123113 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times9}123123113\\\underline{\times\phantom{99999}11317}\\\phantom{\times9}861861791\\\phantom{\times}123123113\phantom{9}\\\phantom{\times}369369339\phantom{99}\\\phantom{\times}123123113\phantom{999}\\\underline{\phantom{\times}123123113\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 123123113 with 1. Write the result 123123113 at the end leaving 4 spaces to the right like this.
\begin{array}{c}\phantom{\times9}123123113\\\underline{\times\phantom{99999}11317}\\\phantom{\times9}861861791\\\phantom{\times}123123113\phantom{9}\\\phantom{\times}369369339\phantom{99}\\\phantom{\times}123123113\phantom{999}\\\underline{\phantom{\times}123123113\phantom{9999}}\\\phantom{\times}1814865917\end{array}
Now add the intermediate results to get final answer.