OK, let's crack this. We're given 684 and our task is to multiply it by 186. Essentially, we'll be adding 684 to itself 186 times.
Step 1: 0 + 684 = 684
Step 2: 684 + 684 = 1368
Step 3: 1368 + 684 = 2052
Step 4: 2052 + 684 = 2736
Step 5: 2736 + 684 = 3420
Step 6: 3420 + 684 = 4104
Step 7: 4104 + 684 = 4788
Step 8: 4788 + 684 = 5472
Step 9: 5472 + 684 = 6156
Step 10: 6156 + 684 = 6840
Step 11: 6840 + 684 = 7524
Step 12: 7524 + 684 = 8208
Step 13: 8208 + 684 = 8892
Step 14: 8892 + 684 = 9576
Step 15: 9576 + 684 = 10260
Step 16: 10260 + 684 = 10944
Step 17: 10944 + 684 = 11628
Step 18: 11628 + 684 = 12312
Step 19: 12312 + 684 = 12996
Step 20: 12996 + 684 = 13680
Step 21: 13680 + 684 = 14364
Step 22: 14364 + 684 = 15048
Step 23: 15048 + 684 = 15732
Step 24: 15732 + 684 = 16416
Step 25: 16416 + 684 = 17100
Step 26: 17100 + 684 = 17784
Step 27: 17784 + 684 = 18468
Step 28: 18468 + 684 = 19152
Step 29: 19152 + 684 = 19836
Step 30: 19836 + 684 = 20520
Step 31: 20520 + 684 = 21204
Step 32: 21204 + 684 = 21888
Step 33: 21888 + 684 = 22572
Step 34: 22572 + 684 = 23256
Step 35: 23256 + 684 = 23940
Step 36: 23940 + 684 = 24624
Step 37: 24624 + 684 = 25308
Step 38: 25308 + 684 = 25992
Step 39: 25992 + 684 = 26676
Step 40: 26676 + 684 = 27360
Step 41: 27360 + 684 = 28044
Step 42: 28044 + 684 = 28728
Step 43: 28728 + 684 = 29412
Step 44: 29412 + 684 = 30096
Step 45: 30096 + 684 = 30780
Step 46: 30780 + 684 = 31464
Step 47: 31464 + 684 = 32148
Step 48: 32148 + 684 = 32832
Step 49: 32832 + 684 = 33516
Step 50: 33516 + 684 = 34200
Step 51: 34200 + 684 = 34884
Step 52: 34884 + 684 = 35568
Step 53: 35568 + 684 = 36252
Step 54: 36252 + 684 = 36936
Step 55: 36936 + 684 = 37620
Step 56: 37620 + 684 = 38304
Step 57: 38304 + 684 = 38988
Step 58: 38988 + 684 = 39672
Step 59: 39672 + 684 = 40356
Step 60: 40356 + 684 = 41040
Step 61: 41040 + 684 = 41724
Step 62: 41724 + 684 = 42408
Step 63: 42408 + 684 = 43092
Step 64: 43092 + 684 = 43776
Step 65: 43776 + 684 = 44460
Step 66: 44460 + 684 = 45144
Step 67: 45144 + 684 = 45828
Step 68: 45828 + 684 = 46512
Step 69: 46512 + 684 = 47196
Step 70: 47196 + 684 = 47880
Step 71: 47880 + 684 = 48564
Step 72: 48564 + 684 = 49248
Step 73: 49248 + 684 = 49932
Step 74: 49932 + 684 = 50616
Step 75: 50616 + 684 = 51300
Step 76: 51300 + 684 = 51984
Step 77: 51984 + 684 = 52668
Step 78: 52668 + 684 = 53352
Step 79: 53352 + 684 = 54036
Step 80: 54036 + 684 = 54720
Step 81: 54720 + 684 = 55404
Step 82: 55404 + 684 = 56088
Step 83: 56088 + 684 = 56772
Step 84: 56772 + 684 = 57456
Step 85: 57456 + 684 = 58140
Step 86: 58140 + 684 = 58824
Step 87: 58824 + 684 = 59508
Step 88: 59508 + 684 = 60192
Step 89: 60192 + 684 = 60876
Step 90: 60876 + 684 = 61560
Step 91: 61560 + 684 = 62244
Step 92: 62244 + 684 = 62928
Step 93: 62928 + 684 = 63612
Step 94: 63612 + 684 = 64296
Step 95: 64296 + 684 = 64980
Step 96: 64980 + 684 = 65664
Step 97: 65664 + 684 = 66348
Step 98: 66348 + 684 = 67032
Step 99: 67032 + 684 = 67716
Step 100: 67716 + 684 = 68400
Step 101: 68400 + 684 = 69084
Step 102: 69084 + 684 = 69768
Step 103: 69768 + 684 = 70452
Step 104: 70452 + 684 = 71136
Step 105: 71136 + 684 = 71820
Step 106: 71820 + 684 = 72504
Step 107: 72504 + 684 = 73188
Step 108: 73188 + 684 = 73872
Step 109: 73872 + 684 = 74556
Step 110: 74556 + 684 = 75240
Step 111: 75240 + 684 = 75924
Step 112: 75924 + 684 = 76608
Step 113: 76608 + 684 = 77292
Step 114: 77292 + 684 = 77976
Step 115: 77976 + 684 = 78660
Step 116: 78660 + 684 = 79344
Step 117: 79344 + 684 = 80028
Step 118: 80028 + 684 = 80712
Step 119: 80712 + 684 = 81396
Step 120: 81396 + 684 = 82080
Step 121: 82080 + 684 = 82764
Step 122: 82764 + 684 = 83448
Step 123: 83448 + 684 = 84132
Step 124: 84132 + 684 = 84816
Step 125: 84816 + 684 = 85500
Step 126: 85500 + 684 = 86184
Step 127: 86184 + 684 = 86868
Step 128: 86868 + 684 = 87552
Step 129: 87552 + 684 = 88236
Step 130: 88236 + 684 = 88920
Step 131: 88920 + 684 = 89604
Step 132: 89604 + 684 = 90288
Step 133: 90288 + 684 = 90972
Step 134: 90972 + 684 = 91656
Step 135: 91656 + 684 = 92340
Step 136: 92340 + 684 = 93024
Step 137: 93024 + 684 = 93708
Step 138: 93708 + 684 = 94392
Step 139: 94392 + 684 = 95076
Step 140: 95076 + 684 = 95760
Step 141: 95760 + 684 = 96444
Step 142: 96444 + 684 = 97128
Step 143: 97128 + 684 = 97812
Step 144: 97812 + 684 = 98496
Step 145: 98496 + 684 = 99180
Step 146: 99180 + 684 = 99864
Step 147: 99864 + 684 = 100548
Step 148: 100548 + 684 = 101232
Step 149: 101232 + 684 = 101916
Step 150: 101916 + 684 = 102600
Step 151: 102600 + 684 = 103284
Step 152: 103284 + 684 = 103968
Step 153: 103968 + 684 = 104652
Step 154: 104652 + 684 = 105336
Step 155: 105336 + 684 = 106020
Step 156: 106020 + 684 = 106704
Step 157: 106704 + 684 = 107388
Step 158: 107388 + 684 = 108072
Step 159: 108072 + 684 = 108756
Step 160: 108756 + 684 = 109440
Step 161: 109440 + 684 = 110124
Step 162: 110124 + 684 = 110808
Step 163: 110808 + 684 = 111492
Step 164: 111492 + 684 = 112176
Step 165: 112176 + 684 = 112860
Step 166: 112860 + 684 = 113544
Step 167: 113544 + 684 = 114228
Step 168: 114228 + 684 = 114912
Step 169: 114912 + 684 = 115596
Step 170: 115596 + 684 = 116280
Step 171: 116280 + 684 = 116964
Step 172: 116964 + 684 = 117648
Step 173: 117648 + 684 = 118332
Step 174: 118332 + 684 = 119016
Step 175: 119016 + 684 = 119700
Step 176: 119700 + 684 = 120384
Step 177: 120384 + 684 = 121068
Step 178: 121068 + 684 = 121752
Step 179: 121752 + 684 = 122436
Step 180: 122436 + 684 = 123120
Step 181: 123120 + 684 = 123804
Step 182: 123804 + 684 = 124488
Step 183: 124488 + 684 = 125172
Step 184: 125172 + 684 = 125856
Step 185: 125856 + 684 = 126540
Step 186: 126540 + 684 = 127224

So, 684*186 = 127224