Let's roll up our sleeves and solve this. We have 317 and we're going to multiply it by 23, essentially adding 317 to itself 23 times.
Step 1: 0 + 317 = 317
Step 2: 317 + 317 = 634
Step 3: 634 + 317 = 951
Step 4: 951 + 317 = 1268
Step 5: 1268 + 317 = 1585
Step 6: 1585 + 317 = 1902
Step 7: 1902 + 317 = 2219
Step 8: 2219 + 317 = 2536
Step 9: 2536 + 317 = 2853
Step 10: 2853 + 317 = 3170
Step 11: 3170 + 317 = 3487
Step 12: 3487 + 317 = 3804
Step 13: 3804 + 317 = 4121
Step 14: 4121 + 317 = 4438
Step 15: 4438 + 317 = 4755
Step 16: 4755 + 317 = 5072
Step 17: 5072 + 317 = 5389
Step 18: 5389 + 317 = 5706
Step 19: 5706 + 317 = 6023
Step 20: 6023 + 317 = 6340
Step 21: 6340 + 317 = 6657
Step 22: 6657 + 317 = 6974
Step 23: 6974 + 317 = 7291

So, 317*23 = 7291