OK, let's work through this together. We're starting with 577 and we're going to multiply it by 11, which means we add 577 to itself 11 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

So, 577*11 = 6347