OK, let's crack this. We're given 577 and our task is to multiply it by 119. Essentially, we'll be adding 577 to itself 119 times.
Step 1: 0 + 577 = 577
Step 2: 577 + 577 = 1154
Step 3: 1154 + 577 = 1731
Step 4: 1731 + 577 = 2308
Step 5: 2308 + 577 = 2885
Step 6: 2885 + 577 = 3462
Step 7: 3462 + 577 = 4039
Step 8: 4039 + 577 = 4616
Step 9: 4616 + 577 = 5193
Step 10: 5193 + 577 = 5770
Step 11: 5770 + 577 = 6347
Step 12: 6347 + 577 = 6924
Step 13: 6924 + 577 = 7501
Step 14: 7501 + 577 = 8078
Step 15: 8078 + 577 = 8655
Step 16: 8655 + 577 = 9232
Step 17: 9232 + 577 = 9809
Step 18: 9809 + 577 = 10386
Step 19: 10386 + 577 = 10963
Step 20: 10963 + 577 = 11540
Step 21: 11540 + 577 = 12117
Step 22: 12117 + 577 = 12694
Step 23: 12694 + 577 = 13271
Step 24: 13271 + 577 = 13848
Step 25: 13848 + 577 = 14425
Step 26: 14425 + 577 = 15002
Step 27: 15002 + 577 = 15579
Step 28: 15579 + 577 = 16156
Step 29: 16156 + 577 = 16733
Step 30: 16733 + 577 = 17310
Step 31: 17310 + 577 = 17887
Step 32: 17887 + 577 = 18464
Step 33: 18464 + 577 = 19041
Step 34: 19041 + 577 = 19618
Step 35: 19618 + 577 = 20195
Step 36: 20195 + 577 = 20772
Step 37: 20772 + 577 = 21349
Step 38: 21349 + 577 = 21926
Step 39: 21926 + 577 = 22503
Step 40: 22503 + 577 = 23080
Step 41: 23080 + 577 = 23657
Step 42: 23657 + 577 = 24234
Step 43: 24234 + 577 = 24811
Step 44: 24811 + 577 = 25388
Step 45: 25388 + 577 = 25965
Step 46: 25965 + 577 = 26542
Step 47: 26542 + 577 = 27119
Step 48: 27119 + 577 = 27696
Step 49: 27696 + 577 = 28273
Step 50: 28273 + 577 = 28850
Step 51: 28850 + 577 = 29427
Step 52: 29427 + 577 = 30004
Step 53: 30004 + 577 = 30581
Step 54: 30581 + 577 = 31158
Step 55: 31158 + 577 = 31735
Step 56: 31735 + 577 = 32312
Step 57: 32312 + 577 = 32889
Step 58: 32889 + 577 = 33466
Step 59: 33466 + 577 = 34043
Step 60: 34043 + 577 = 34620
Step 61: 34620 + 577 = 35197
Step 62: 35197 + 577 = 35774
Step 63: 35774 + 577 = 36351
Step 64: 36351 + 577 = 36928
Step 65: 36928 + 577 = 37505
Step 66: 37505 + 577 = 38082
Step 67: 38082 + 577 = 38659
Step 68: 38659 + 577 = 39236
Step 69: 39236 + 577 = 39813
Step 70: 39813 + 577 = 40390
Step 71: 40390 + 577 = 40967
Step 72: 40967 + 577 = 41544
Step 73: 41544 + 577 = 42121
Step 74: 42121 + 577 = 42698
Step 75: 42698 + 577 = 43275
Step 76: 43275 + 577 = 43852
Step 77: 43852 + 577 = 44429
Step 78: 44429 + 577 = 45006
Step 79: 45006 + 577 = 45583
Step 80: 45583 + 577 = 46160
Step 81: 46160 + 577 = 46737
Step 82: 46737 + 577 = 47314
Step 83: 47314 + 577 = 47891
Step 84: 47891 + 577 = 48468
Step 85: 48468 + 577 = 49045
Step 86: 49045 + 577 = 49622
Step 87: 49622 + 577 = 50199
Step 88: 50199 + 577 = 50776
Step 89: 50776 + 577 = 51353
Step 90: 51353 + 577 = 51930
Step 91: 51930 + 577 = 52507
Step 92: 52507 + 577 = 53084
Step 93: 53084 + 577 = 53661
Step 94: 53661 + 577 = 54238
Step 95: 54238 + 577 = 54815
Step 96: 54815 + 577 = 55392
Step 97: 55392 + 577 = 55969
Step 98: 55969 + 577 = 56546
Step 99: 56546 + 577 = 57123
Step 100: 57123 + 577 = 57700
Step 101: 57700 + 577 = 58277
Step 102: 58277 + 577 = 58854
Step 103: 58854 + 577 = 59431
Step 104: 59431 + 577 = 60008
Step 105: 60008 + 577 = 60585
Step 106: 60585 + 577 = 61162
Step 107: 61162 + 577 = 61739
Step 108: 61739 + 577 = 62316
Step 109: 62316 + 577 = 62893
Step 110: 62893 + 577 = 63470
Step 111: 63470 + 577 = 64047
Step 112: 64047 + 577 = 64624
Step 113: 64624 + 577 = 65201
Step 114: 65201 + 577 = 65778
Step 115: 65778 + 577 = 66355
Step 116: 66355 + 577 = 66932
Step 117: 66932 + 577 = 67509
Step 118: 67509 + 577 = 68086
Step 119: 68086 + 577 = 68663

So, 577*119 = 68663