Now multiply the first number with the $1^{st}$ digit in $2^{nd}$ number to get intermediate results. That is Multiply 6303 with 5. Write the result 31515 at the end leaving 0 spaces to the right like this.
Now multiply the first number with the $2^{nd}$ digit in $2^{nd}$ number to get intermediate results. That is Multiply 6303 with 7. Write the result 44121 at the end leaving 1 spaces to the right like this.