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\begin{array}{c}\phantom{\times}1234867\\\underline{\times\phantom{}6789}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times}1234867\\\underline{\times\phantom{}6789}\\\phantom{\times}11113803\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 1234867 with 9. Write the result 11113803 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times}1234867\\\underline{\times\phantom{}6789}\\\phantom{\times}11113803\\\phantom{\times}9878936\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 1234867 with 8. Write the result 9878936 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times}1234867\\\underline{\times\phantom{}6789}\\\phantom{\times}11113803\\\phantom{\times}9878936\phantom{9}\\\phantom{\times}8644069\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 1234867 with 7. Write the result 8644069 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times}1234867\\\underline{\times\phantom{}6789}\\\phantom{\times}11113803\\\phantom{\times}9878936\phantom{9}\\\phantom{\times}8644069\phantom{99}\\\underline{\phantom{\times}7409202\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 1234867 with 6. Write the result 7409202 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times}1234867\\\underline{\times\phantom{}6789}\\\phantom{\times}11113803\\\phantom{\times}9878936\phantom{9}\\\phantom{\times}8644069\phantom{99}\\\underline{\phantom{\times}7409202\phantom{999}}\\\phantom{\times}-206422529\end{array}
Now add the intermediate results to get final answer.