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\begin{array}{c}\phantom{\times9999}4999\\\underline{\times\phantom{9999}6842}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times9999}4999\\\underline{\times\phantom{9999}6842}\\\phantom{\times9999}9998\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 4999 with 2. Write the result 9998 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}4999\\\underline{\times\phantom{9999}6842}\\\phantom{\times9999}9998\\\phantom{\times99}19996\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 4999 with 4. Write the result 19996 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}4999\\\underline{\times\phantom{9999}6842}\\\phantom{\times9999}9998\\\phantom{\times99}19996\phantom{9}\\\phantom{\times9}39992\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 4999 with 8. Write the result 39992 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}4999\\\underline{\times\phantom{9999}6842}\\\phantom{\times9999}9998\\\phantom{\times99}19996\phantom{9}\\\phantom{\times9}39992\phantom{99}\\\underline{\phantom{\times}29994\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 4999 with 6. Write the result 29994 at the end leaving 3 spaces to the right like this.
\begin{array}{c}\phantom{\times9999}4999\\\underline{\times\phantom{9999}6842}\\\phantom{\times9999}9998\\\phantom{\times99}19996\phantom{9}\\\phantom{\times9}39992\phantom{99}\\\underline{\phantom{\times}29994\phantom{999}}\\\phantom{\times}34203158\end{array}
Now add the intermediate results to get final answer.