Let's roll up our sleeves and solve this. We have 578 and we're going to multiply it by 66, essentially adding 578 to itself 66 times.
Step 1: 0 + 578 = 578
Step 2: 578 + 578 = 1156
Step 3: 1156 + 578 = 1734
Step 4: 1734 + 578 = 2312
Step 5: 2312 + 578 = 2890
Step 6: 2890 + 578 = 3468
Step 7: 3468 + 578 = 4046
Step 8: 4046 + 578 = 4624
Step 9: 4624 + 578 = 5202
Step 10: 5202 + 578 = 5780
Step 11: 5780 + 578 = 6358
Step 12: 6358 + 578 = 6936
Step 13: 6936 + 578 = 7514
Step 14: 7514 + 578 = 8092
Step 15: 8092 + 578 = 8670
Step 16: 8670 + 578 = 9248
Step 17: 9248 + 578 = 9826
Step 18: 9826 + 578 = 10404
Step 19: 10404 + 578 = 10982
Step 20: 10982 + 578 = 11560
Step 21: 11560 + 578 = 12138
Step 22: 12138 + 578 = 12716
Step 23: 12716 + 578 = 13294
Step 24: 13294 + 578 = 13872
Step 25: 13872 + 578 = 14450
Step 26: 14450 + 578 = 15028
Step 27: 15028 + 578 = 15606
Step 28: 15606 + 578 = 16184
Step 29: 16184 + 578 = 16762
Step 30: 16762 + 578 = 17340
Step 31: 17340 + 578 = 17918
Step 32: 17918 + 578 = 18496
Step 33: 18496 + 578 = 19074
Step 34: 19074 + 578 = 19652
Step 35: 19652 + 578 = 20230
Step 36: 20230 + 578 = 20808
Step 37: 20808 + 578 = 21386
Step 38: 21386 + 578 = 21964
Step 39: 21964 + 578 = 22542
Step 40: 22542 + 578 = 23120
Step 41: 23120 + 578 = 23698
Step 42: 23698 + 578 = 24276
Step 43: 24276 + 578 = 24854
Step 44: 24854 + 578 = 25432
Step 45: 25432 + 578 = 26010
Step 46: 26010 + 578 = 26588
Step 47: 26588 + 578 = 27166
Step 48: 27166 + 578 = 27744
Step 49: 27744 + 578 = 28322
Step 50: 28322 + 578 = 28900
Step 51: 28900 + 578 = 29478
Step 52: 29478 + 578 = 30056
Step 53: 30056 + 578 = 30634
Step 54: 30634 + 578 = 31212
Step 55: 31212 + 578 = 31790
Step 56: 31790 + 578 = 32368
Step 57: 32368 + 578 = 32946
Step 58: 32946 + 578 = 33524
Step 59: 33524 + 578 = 34102
Step 60: 34102 + 578 = 34680
Step 61: 34680 + 578 = 35258
Step 62: 35258 + 578 = 35836
Step 63: 35836 + 578 = 36414
Step 64: 36414 + 578 = 36992
Step 65: 36992 + 578 = 37570
Step 66: 37570 + 578 = 38148

So, 578*66 = 38148