OK, let's crack this. We're given 346 and our task is to multiply it by 111. Essentially, we'll be adding 346 to itself 111 times.
Step 1: 0 + 346 = 346
Step 2: 346 + 346 = 692
Step 3: 692 + 346 = 1038
Step 4: 1038 + 346 = 1384
Step 5: 1384 + 346 = 1730
Step 6: 1730 + 346 = 2076
Step 7: 2076 + 346 = 2422
Step 8: 2422 + 346 = 2768
Step 9: 2768 + 346 = 3114
Step 10: 3114 + 346 = 3460
Step 11: 3460 + 346 = 3806
Step 12: 3806 + 346 = 4152
Step 13: 4152 + 346 = 4498
Step 14: 4498 + 346 = 4844
Step 15: 4844 + 346 = 5190
Step 16: 5190 + 346 = 5536
Step 17: 5536 + 346 = 5882
Step 18: 5882 + 346 = 6228
Step 19: 6228 + 346 = 6574
Step 20: 6574 + 346 = 6920
Step 21: 6920 + 346 = 7266
Step 22: 7266 + 346 = 7612
Step 23: 7612 + 346 = 7958
Step 24: 7958 + 346 = 8304
Step 25: 8304 + 346 = 8650
Step 26: 8650 + 346 = 8996
Step 27: 8996 + 346 = 9342
Step 28: 9342 + 346 = 9688
Step 29: 9688 + 346 = 10034
Step 30: 10034 + 346 = 10380
Step 31: 10380 + 346 = 10726
Step 32: 10726 + 346 = 11072
Step 33: 11072 + 346 = 11418
Step 34: 11418 + 346 = 11764
Step 35: 11764 + 346 = 12110
Step 36: 12110 + 346 = 12456
Step 37: 12456 + 346 = 12802
Step 38: 12802 + 346 = 13148
Step 39: 13148 + 346 = 13494
Step 40: 13494 + 346 = 13840
Step 41: 13840 + 346 = 14186
Step 42: 14186 + 346 = 14532
Step 43: 14532 + 346 = 14878
Step 44: 14878 + 346 = 15224
Step 45: 15224 + 346 = 15570
Step 46: 15570 + 346 = 15916
Step 47: 15916 + 346 = 16262
Step 48: 16262 + 346 = 16608
Step 49: 16608 + 346 = 16954
Step 50: 16954 + 346 = 17300
Step 51: 17300 + 346 = 17646
Step 52: 17646 + 346 = 17992
Step 53: 17992 + 346 = 18338
Step 54: 18338 + 346 = 18684
Step 55: 18684 + 346 = 19030
Step 56: 19030 + 346 = 19376
Step 57: 19376 + 346 = 19722
Step 58: 19722 + 346 = 20068
Step 59: 20068 + 346 = 20414
Step 60: 20414 + 346 = 20760
Step 61: 20760 + 346 = 21106
Step 62: 21106 + 346 = 21452
Step 63: 21452 + 346 = 21798
Step 64: 21798 + 346 = 22144
Step 65: 22144 + 346 = 22490
Step 66: 22490 + 346 = 22836
Step 67: 22836 + 346 = 23182
Step 68: 23182 + 346 = 23528
Step 69: 23528 + 346 = 23874
Step 70: 23874 + 346 = 24220
Step 71: 24220 + 346 = 24566
Step 72: 24566 + 346 = 24912
Step 73: 24912 + 346 = 25258
Step 74: 25258 + 346 = 25604
Step 75: 25604 + 346 = 25950
Step 76: 25950 + 346 = 26296
Step 77: 26296 + 346 = 26642
Step 78: 26642 + 346 = 26988
Step 79: 26988 + 346 = 27334
Step 80: 27334 + 346 = 27680
Step 81: 27680 + 346 = 28026
Step 82: 28026 + 346 = 28372
Step 83: 28372 + 346 = 28718
Step 84: 28718 + 346 = 29064
Step 85: 29064 + 346 = 29410
Step 86: 29410 + 346 = 29756
Step 87: 29756 + 346 = 30102
Step 88: 30102 + 346 = 30448
Step 89: 30448 + 346 = 30794
Step 90: 30794 + 346 = 31140
Step 91: 31140 + 346 = 31486
Step 92: 31486 + 346 = 31832
Step 93: 31832 + 346 = 32178
Step 94: 32178 + 346 = 32524
Step 95: 32524 + 346 = 32870
Step 96: 32870 + 346 = 33216
Step 97: 33216 + 346 = 33562
Step 98: 33562 + 346 = 33908
Step 99: 33908 + 346 = 34254
Step 100: 34254 + 346 = 34600
Step 101: 34600 + 346 = 34946
Step 102: 34946 + 346 = 35292
Step 103: 35292 + 346 = 35638
Step 104: 35638 + 346 = 35984
Step 105: 35984 + 346 = 36330
Step 106: 36330 + 346 = 36676
Step 107: 36676 + 346 = 37022
Step 108: 37022 + 346 = 37368
Step 109: 37368 + 346 = 37714
Step 110: 37714 + 346 = 38060
Step 111: 38060 + 346 = 38406

So, 346*111 = 38406