Let's roll up our sleeves and solve this. We have 343 and we're going to multiply it by 34, essentially adding 343 to itself 34 times.
Step 1: 0 + 343 = 343
Step 2: 343 + 343 = 686
Step 3: 686 + 343 = 1029
Step 4: 1029 + 343 = 1372
Step 5: 1372 + 343 = 1715
Step 6: 1715 + 343 = 2058
Step 7: 2058 + 343 = 2401
Step 8: 2401 + 343 = 2744
Step 9: 2744 + 343 = 3087
Step 10: 3087 + 343 = 3430
Step 11: 3430 + 343 = 3773
Step 12: 3773 + 343 = 4116
Step 13: 4116 + 343 = 4459
Step 14: 4459 + 343 = 4802
Step 15: 4802 + 343 = 5145
Step 16: 5145 + 343 = 5488
Step 17: 5488 + 343 = 5831
Step 18: 5831 + 343 = 6174
Step 19: 6174 + 343 = 6517
Step 20: 6517 + 343 = 6860
Step 21: 6860 + 343 = 7203
Step 22: 7203 + 343 = 7546
Step 23: 7546 + 343 = 7889
Step 24: 7889 + 343 = 8232
Step 25: 8232 + 343 = 8575
Step 26: 8575 + 343 = 8918
Step 27: 8918 + 343 = 9261
Step 28: 9261 + 343 = 9604
Step 29: 9604 + 343 = 9947
Step 30: 9947 + 343 = 10290
Step 31: 10290 + 343 = 10633
Step 32: 10633 + 343 = 10976
Step 33: 10976 + 343 = 11319
Step 34: 11319 + 343 = 11662

So, 343*34 = 11662