The following example explains the diagonal method of multiplying numbers.  Study it and you will see the pattern.

Explanation: 7*3=21 and this is why the digits 2 and 1 are written in the corresponding square and the same with the other numbers.  After all the squares are filled you simply add the digits in each diangonal and if the answer is more than 9 you transfer the carry to the next diagonal.
The sum of the first diagonal = 7
The sum of the second diagonal = 7
The sum of the first diagonal = 11 (write 1 and carry 1)
The sum of the first diagonal  (including the carry)= 18 (write 8 carry 1)
The sum of the first diagonal (including the carry) = 6 (inclusing the carry)

Thus the answer is 863*79=68177

If needed, study the following example and see if you can get the product 343*268=91924

Then practice to get the correct answer: