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\begin{array}{c}\phantom{\times999}34\\\underline{\times\phantom{9}1800}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times999}34\\\underline{\times\phantom{9}1800}\\\phantom{\times99999}0\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 34 with 0. Write the result 0 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times999}34\\\underline{\times\phantom{9}1800}\\\phantom{\times99999}0\\\phantom{\times9999}0\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 34 with 0. Write the result 0 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times999}34\\\underline{\times\phantom{9}1800}\\\phantom{\times99999}0\\\phantom{\times9999}0\phantom{9}\\\phantom{\times}272\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 34 with 8. Write the result 272 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times999}34\\\underline{\times\phantom{9}1800}\\\phantom{\times99999}0\\\phantom{\times9999}0\phantom{9}\\\phantom{\times}272\phantom{99}\\\underline{\phantom{\times}34\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 34 with 1. Write the result 34 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times999}34\\\underline{\times\phantom{9}1800}\\\phantom{\times99999}0\\\phantom{\times9999}0\phantom{9}\\\phantom{\times}272\phantom{99}\\\underline{\phantom{\times}34\phantom{999}}\\\phantom{\times}61200\end{array}
Now add the intermediate results to get final answer.