OK, let's crack this. We're given 674 and our task is to multiply it by 177. Essentially, we'll be adding 674 to itself 177 times.
Step 1: 0 + 674 = 674
Step 2: 674 + 674 = 1348
Step 3: 1348 + 674 = 2022
Step 4: 2022 + 674 = 2696
Step 5: 2696 + 674 = 3370
Step 6: 3370 + 674 = 4044
Step 7: 4044 + 674 = 4718
Step 8: 4718 + 674 = 5392
Step 9: 5392 + 674 = 6066
Step 10: 6066 + 674 = 6740
Step 11: 6740 + 674 = 7414
Step 12: 7414 + 674 = 8088
Step 13: 8088 + 674 = 8762
Step 14: 8762 + 674 = 9436
Step 15: 9436 + 674 = 10110
Step 16: 10110 + 674 = 10784
Step 17: 10784 + 674 = 11458
Step 18: 11458 + 674 = 12132
Step 19: 12132 + 674 = 12806
Step 20: 12806 + 674 = 13480
Step 21: 13480 + 674 = 14154
Step 22: 14154 + 674 = 14828
Step 23: 14828 + 674 = 15502
Step 24: 15502 + 674 = 16176
Step 25: 16176 + 674 = 16850
Step 26: 16850 + 674 = 17524
Step 27: 17524 + 674 = 18198
Step 28: 18198 + 674 = 18872
Step 29: 18872 + 674 = 19546
Step 30: 19546 + 674 = 20220
Step 31: 20220 + 674 = 20894
Step 32: 20894 + 674 = 21568
Step 33: 21568 + 674 = 22242
Step 34: 22242 + 674 = 22916
Step 35: 22916 + 674 = 23590
Step 36: 23590 + 674 = 24264
Step 37: 24264 + 674 = 24938
Step 38: 24938 + 674 = 25612
Step 39: 25612 + 674 = 26286
Step 40: 26286 + 674 = 26960
Step 41: 26960 + 674 = 27634
Step 42: 27634 + 674 = 28308
Step 43: 28308 + 674 = 28982
Step 44: 28982 + 674 = 29656
Step 45: 29656 + 674 = 30330
Step 46: 30330 + 674 = 31004
Step 47: 31004 + 674 = 31678
Step 48: 31678 + 674 = 32352
Step 49: 32352 + 674 = 33026
Step 50: 33026 + 674 = 33700
Step 51: 33700 + 674 = 34374
Step 52: 34374 + 674 = 35048
Step 53: 35048 + 674 = 35722
Step 54: 35722 + 674 = 36396
Step 55: 36396 + 674 = 37070
Step 56: 37070 + 674 = 37744
Step 57: 37744 + 674 = 38418
Step 58: 38418 + 674 = 39092
Step 59: 39092 + 674 = 39766
Step 60: 39766 + 674 = 40440
Step 61: 40440 + 674 = 41114
Step 62: 41114 + 674 = 41788
Step 63: 41788 + 674 = 42462
Step 64: 42462 + 674 = 43136
Step 65: 43136 + 674 = 43810
Step 66: 43810 + 674 = 44484
Step 67: 44484 + 674 = 45158
Step 68: 45158 + 674 = 45832
Step 69: 45832 + 674 = 46506
Step 70: 46506 + 674 = 47180
Step 71: 47180 + 674 = 47854
Step 72: 47854 + 674 = 48528
Step 73: 48528 + 674 = 49202
Step 74: 49202 + 674 = 49876
Step 75: 49876 + 674 = 50550
Step 76: 50550 + 674 = 51224
Step 77: 51224 + 674 = 51898
Step 78: 51898 + 674 = 52572
Step 79: 52572 + 674 = 53246
Step 80: 53246 + 674 = 53920
Step 81: 53920 + 674 = 54594
Step 82: 54594 + 674 = 55268
Step 83: 55268 + 674 = 55942
Step 84: 55942 + 674 = 56616
Step 85: 56616 + 674 = 57290
Step 86: 57290 + 674 = 57964
Step 87: 57964 + 674 = 58638
Step 88: 58638 + 674 = 59312
Step 89: 59312 + 674 = 59986
Step 90: 59986 + 674 = 60660
Step 91: 60660 + 674 = 61334
Step 92: 61334 + 674 = 62008
Step 93: 62008 + 674 = 62682
Step 94: 62682 + 674 = 63356
Step 95: 63356 + 674 = 64030
Step 96: 64030 + 674 = 64704
Step 97: 64704 + 674 = 65378
Step 98: 65378 + 674 = 66052
Step 99: 66052 + 674 = 66726
Step 100: 66726 + 674 = 67400
Step 101: 67400 + 674 = 68074
Step 102: 68074 + 674 = 68748
Step 103: 68748 + 674 = 69422
Step 104: 69422 + 674 = 70096
Step 105: 70096 + 674 = 70770
Step 106: 70770 + 674 = 71444
Step 107: 71444 + 674 = 72118
Step 108: 72118 + 674 = 72792
Step 109: 72792 + 674 = 73466
Step 110: 73466 + 674 = 74140
Step 111: 74140 + 674 = 74814
Step 112: 74814 + 674 = 75488
Step 113: 75488 + 674 = 76162
Step 114: 76162 + 674 = 76836
Step 115: 76836 + 674 = 77510
Step 116: 77510 + 674 = 78184
Step 117: 78184 + 674 = 78858
Step 118: 78858 + 674 = 79532
Step 119: 79532 + 674 = 80206
Step 120: 80206 + 674 = 80880
Step 121: 80880 + 674 = 81554
Step 122: 81554 + 674 = 82228
Step 123: 82228 + 674 = 82902
Step 124: 82902 + 674 = 83576
Step 125: 83576 + 674 = 84250
Step 126: 84250 + 674 = 84924
Step 127: 84924 + 674 = 85598
Step 128: 85598 + 674 = 86272
Step 129: 86272 + 674 = 86946
Step 130: 86946 + 674 = 87620
Step 131: 87620 + 674 = 88294
Step 132: 88294 + 674 = 88968
Step 133: 88968 + 674 = 89642
Step 134: 89642 + 674 = 90316
Step 135: 90316 + 674 = 90990
Step 136: 90990 + 674 = 91664
Step 137: 91664 + 674 = 92338
Step 138: 92338 + 674 = 93012
Step 139: 93012 + 674 = 93686
Step 140: 93686 + 674 = 94360
Step 141: 94360 + 674 = 95034
Step 142: 95034 + 674 = 95708
Step 143: 95708 + 674 = 96382
Step 144: 96382 + 674 = 97056
Step 145: 97056 + 674 = 97730
Step 146: 97730 + 674 = 98404
Step 147: 98404 + 674 = 99078
Step 148: 99078 + 674 = 99752
Step 149: 99752 + 674 = 100426
Step 150: 100426 + 674 = 101100
Step 151: 101100 + 674 = 101774
Step 152: 101774 + 674 = 102448
Step 153: 102448 + 674 = 103122
Step 154: 103122 + 674 = 103796
Step 155: 103796 + 674 = 104470
Step 156: 104470 + 674 = 105144
Step 157: 105144 + 674 = 105818
Step 158: 105818 + 674 = 106492
Step 159: 106492 + 674 = 107166
Step 160: 107166 + 674 = 107840
Step 161: 107840 + 674 = 108514
Step 162: 108514 + 674 = 109188
Step 163: 109188 + 674 = 109862
Step 164: 109862 + 674 = 110536
Step 165: 110536 + 674 = 111210
Step 166: 111210 + 674 = 111884
Step 167: 111884 + 674 = 112558
Step 168: 112558 + 674 = 113232
Step 169: 113232 + 674 = 113906
Step 170: 113906 + 674 = 114580
Step 171: 114580 + 674 = 115254
Step 172: 115254 + 674 = 115928
Step 173: 115928 + 674 = 116602
Step 174: 116602 + 674 = 117276
Step 175: 117276 + 674 = 117950
Step 176: 117950 + 674 = 118624
Step 177: 118624 + 674 = 119298

So, 674*177 = 119298