Start with the right-most digit, 6. Multiply 7 with 6 and add the neighbor (none in this case, as 6 is the right-most digit). We get 42.
Write down 2, and carry the 4. -----> 2
Move left to the next digit, 4. Multiply 7 with 4 to get 28, add the neighbor to right 6, to get 34, and add the carry 4, to get 38.
Write down the 8, and carry the 3. -----> 82
Move left to the next digit, 3. Multiply 7 with 3 to get 21. Add the neighbor, 4, and we get 25. Add the carry 3, to get 28.
Write down the 8, and carry the 2. -----> 882
Now add the carry 2 to the left most digit 3 which gives us 5. Finally, Write down 5. -----> 5882
So, our answer is 5882