Let's roll up our sleeves and solve this. We have 509 and we're going to multiply it by 9, essentially adding 509 to itself 9 times.
Step 1: 0 + 509 = 509
Step 2: 509 + 509 = 1018
Step 3: 1018 + 509 = 1527
Step 4: 1527 + 509 = 2036
Step 5: 2036 + 509 = 2545
Step 6: 2545 + 509 = 3054
Step 7: 3054 + 509 = 3563
Step 8: 3563 + 509 = 4072
Step 9: 4072 + 509 = 4581

So, 509*9 = 4581