OK, let's crack this. We're given 419 and our task is to multiply it by 188. Essentially, we'll be adding 419 to itself 188 times.
Step 1: 0 + 419 = 419
Step 2: 419 + 419 = 838
Step 3: 838 + 419 = 1257
Step 4: 1257 + 419 = 1676
Step 5: 1676 + 419 = 2095
Step 6: 2095 + 419 = 2514
Step 7: 2514 + 419 = 2933
Step 8: 2933 + 419 = 3352
Step 9: 3352 + 419 = 3771
Step 10: 3771 + 419 = 4190
Step 11: 4190 + 419 = 4609
Step 12: 4609 + 419 = 5028
Step 13: 5028 + 419 = 5447
Step 14: 5447 + 419 = 5866
Step 15: 5866 + 419 = 6285
Step 16: 6285 + 419 = 6704
Step 17: 6704 + 419 = 7123
Step 18: 7123 + 419 = 7542
Step 19: 7542 + 419 = 7961
Step 20: 7961 + 419 = 8380
Step 21: 8380 + 419 = 8799
Step 22: 8799 + 419 = 9218
Step 23: 9218 + 419 = 9637
Step 24: 9637 + 419 = 10056
Step 25: 10056 + 419 = 10475
Step 26: 10475 + 419 = 10894
Step 27: 10894 + 419 = 11313
Step 28: 11313 + 419 = 11732
Step 29: 11732 + 419 = 12151
Step 30: 12151 + 419 = 12570
Step 31: 12570 + 419 = 12989
Step 32: 12989 + 419 = 13408
Step 33: 13408 + 419 = 13827
Step 34: 13827 + 419 = 14246
Step 35: 14246 + 419 = 14665
Step 36: 14665 + 419 = 15084
Step 37: 15084 + 419 = 15503
Step 38: 15503 + 419 = 15922
Step 39: 15922 + 419 = 16341
Step 40: 16341 + 419 = 16760
Step 41: 16760 + 419 = 17179
Step 42: 17179 + 419 = 17598
Step 43: 17598 + 419 = 18017
Step 44: 18017 + 419 = 18436
Step 45: 18436 + 419 = 18855
Step 46: 18855 + 419 = 19274
Step 47: 19274 + 419 = 19693
Step 48: 19693 + 419 = 20112
Step 49: 20112 + 419 = 20531
Step 50: 20531 + 419 = 20950
Step 51: 20950 + 419 = 21369
Step 52: 21369 + 419 = 21788
Step 53: 21788 + 419 = 22207
Step 54: 22207 + 419 = 22626
Step 55: 22626 + 419 = 23045
Step 56: 23045 + 419 = 23464
Step 57: 23464 + 419 = 23883
Step 58: 23883 + 419 = 24302
Step 59: 24302 + 419 = 24721
Step 60: 24721 + 419 = 25140
Step 61: 25140 + 419 = 25559
Step 62: 25559 + 419 = 25978
Step 63: 25978 + 419 = 26397
Step 64: 26397 + 419 = 26816
Step 65: 26816 + 419 = 27235
Step 66: 27235 + 419 = 27654
Step 67: 27654 + 419 = 28073
Step 68: 28073 + 419 = 28492
Step 69: 28492 + 419 = 28911
Step 70: 28911 + 419 = 29330
Step 71: 29330 + 419 = 29749
Step 72: 29749 + 419 = 30168
Step 73: 30168 + 419 = 30587
Step 74: 30587 + 419 = 31006
Step 75: 31006 + 419 = 31425
Step 76: 31425 + 419 = 31844
Step 77: 31844 + 419 = 32263
Step 78: 32263 + 419 = 32682
Step 79: 32682 + 419 = 33101
Step 80: 33101 + 419 = 33520
Step 81: 33520 + 419 = 33939
Step 82: 33939 + 419 = 34358
Step 83: 34358 + 419 = 34777
Step 84: 34777 + 419 = 35196
Step 85: 35196 + 419 = 35615
Step 86: 35615 + 419 = 36034
Step 87: 36034 + 419 = 36453
Step 88: 36453 + 419 = 36872
Step 89: 36872 + 419 = 37291
Step 90: 37291 + 419 = 37710
Step 91: 37710 + 419 = 38129
Step 92: 38129 + 419 = 38548
Step 93: 38548 + 419 = 38967
Step 94: 38967 + 419 = 39386
Step 95: 39386 + 419 = 39805
Step 96: 39805 + 419 = 40224
Step 97: 40224 + 419 = 40643
Step 98: 40643 + 419 = 41062
Step 99: 41062 + 419 = 41481
Step 100: 41481 + 419 = 41900
Step 101: 41900 + 419 = 42319
Step 102: 42319 + 419 = 42738
Step 103: 42738 + 419 = 43157
Step 104: 43157 + 419 = 43576
Step 105: 43576 + 419 = 43995
Step 106: 43995 + 419 = 44414
Step 107: 44414 + 419 = 44833
Step 108: 44833 + 419 = 45252
Step 109: 45252 + 419 = 45671
Step 110: 45671 + 419 = 46090
Step 111: 46090 + 419 = 46509
Step 112: 46509 + 419 = 46928
Step 113: 46928 + 419 = 47347
Step 114: 47347 + 419 = 47766
Step 115: 47766 + 419 = 48185
Step 116: 48185 + 419 = 48604
Step 117: 48604 + 419 = 49023
Step 118: 49023 + 419 = 49442
Step 119: 49442 + 419 = 49861
Step 120: 49861 + 419 = 50280
Step 121: 50280 + 419 = 50699
Step 122: 50699 + 419 = 51118
Step 123: 51118 + 419 = 51537
Step 124: 51537 + 419 = 51956
Step 125: 51956 + 419 = 52375
Step 126: 52375 + 419 = 52794
Step 127: 52794 + 419 = 53213
Step 128: 53213 + 419 = 53632
Step 129: 53632 + 419 = 54051
Step 130: 54051 + 419 = 54470
Step 131: 54470 + 419 = 54889
Step 132: 54889 + 419 = 55308
Step 133: 55308 + 419 = 55727
Step 134: 55727 + 419 = 56146
Step 135: 56146 + 419 = 56565
Step 136: 56565 + 419 = 56984
Step 137: 56984 + 419 = 57403
Step 138: 57403 + 419 = 57822
Step 139: 57822 + 419 = 58241
Step 140: 58241 + 419 = 58660
Step 141: 58660 + 419 = 59079
Step 142: 59079 + 419 = 59498
Step 143: 59498 + 419 = 59917
Step 144: 59917 + 419 = 60336
Step 145: 60336 + 419 = 60755
Step 146: 60755 + 419 = 61174
Step 147: 61174 + 419 = 61593
Step 148: 61593 + 419 = 62012
Step 149: 62012 + 419 = 62431
Step 150: 62431 + 419 = 62850
Step 151: 62850 + 419 = 63269
Step 152: 63269 + 419 = 63688
Step 153: 63688 + 419 = 64107
Step 154: 64107 + 419 = 64526
Step 155: 64526 + 419 = 64945
Step 156: 64945 + 419 = 65364
Step 157: 65364 + 419 = 65783
Step 158: 65783 + 419 = 66202
Step 159: 66202 + 419 = 66621
Step 160: 66621 + 419 = 67040
Step 161: 67040 + 419 = 67459
Step 162: 67459 + 419 = 67878
Step 163: 67878 + 419 = 68297
Step 164: 68297 + 419 = 68716
Step 165: 68716 + 419 = 69135
Step 166: 69135 + 419 = 69554
Step 167: 69554 + 419 = 69973
Step 168: 69973 + 419 = 70392
Step 169: 70392 + 419 = 70811
Step 170: 70811 + 419 = 71230
Step 171: 71230 + 419 = 71649
Step 172: 71649 + 419 = 72068
Step 173: 72068 + 419 = 72487
Step 174: 72487 + 419 = 72906
Step 175: 72906 + 419 = 73325
Step 176: 73325 + 419 = 73744
Step 177: 73744 + 419 = 74163
Step 178: 74163 + 419 = 74582
Step 179: 74582 + 419 = 75001
Step 180: 75001 + 419 = 75420
Step 181: 75420 + 419 = 75839
Step 182: 75839 + 419 = 76258
Step 183: 76258 + 419 = 76677
Step 184: 76677 + 419 = 77096
Step 185: 77096 + 419 = 77515
Step 186: 77515 + 419 = 77934
Step 187: 77934 + 419 = 78353
Step 188: 78353 + 419 = 78772

So, 419*188 = 78772