Let's roll up our sleeves and solve this. We have 369 and we're going to multiply it by 34, essentially adding 369 to itself 34 times.
Step 1: 0 + 369 = 369
Step 2: 369 + 369 = 738
Step 3: 738 + 369 = 1107
Step 4: 1107 + 369 = 1476
Step 5: 1476 + 369 = 1845
Step 6: 1845 + 369 = 2214
Step 7: 2214 + 369 = 2583
Step 8: 2583 + 369 = 2952
Step 9: 2952 + 369 = 3321
Step 10: 3321 + 369 = 3690
Step 11: 3690 + 369 = 4059
Step 12: 4059 + 369 = 4428
Step 13: 4428 + 369 = 4797
Step 14: 4797 + 369 = 5166
Step 15: 5166 + 369 = 5535
Step 16: 5535 + 369 = 5904
Step 17: 5904 + 369 = 6273
Step 18: 6273 + 369 = 6642
Step 19: 6642 + 369 = 7011
Step 20: 7011 + 369 = 7380
Step 21: 7380 + 369 = 7749
Step 22: 7749 + 369 = 8118
Step 23: 8118 + 369 = 8487
Step 24: 8487 + 369 = 8856
Step 25: 8856 + 369 = 9225
Step 26: 9225 + 369 = 9594
Step 27: 9594 + 369 = 9963
Step 28: 9963 + 369 = 10332
Step 29: 10332 + 369 = 10701
Step 30: 10701 + 369 = 11070
Step 31: 11070 + 369 = 11439
Step 32: 11439 + 369 = 11808
Step 33: 11808 + 369 = 12177
Step 34: 12177 + 369 = 12546

So, 369*34 = 12546