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\begin{array}{c}\phantom{\times999}617\\\underline{\times\phantom{999}362}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times999}617\\\underline{\times\phantom{999}362}\\\phantom{\times99}1234\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 617 with 2. Write the result 1234 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times999}617\\\underline{\times\phantom{999}362}\\\phantom{\times99}1234\\\phantom{\times9}3702\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 617 with 6. Write the result 3702 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times999}617\\\underline{\times\phantom{999}362}\\\phantom{\times99}1234\\\phantom{\times9}3702\phantom{9}\\\underline{\phantom{\times}1851\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 617 with 3. Write the result 1851 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times999}617\\\underline{\times\phantom{999}362}\\\phantom{\times99}1234\\\phantom{\times9}3702\phantom{9}\\\underline{\phantom{\times}1851\phantom{99}}\\\phantom{\times}223354\end{array}
Now add the intermediate results to get final answer.