Let's roll up our sleeves and solve this. We have 303 and we're going to multiply it by 23, essentially adding 303 to itself 23 times.
Step 1: 0 + 303 = 303
Step 2: 303 + 303 = 606
Step 3: 606 + 303 = 909
Step 4: 909 + 303 = 1212
Step 5: 1212 + 303 = 1515
Step 6: 1515 + 303 = 1818
Step 7: 1818 + 303 = 2121
Step 8: 2121 + 303 = 2424
Step 9: 2424 + 303 = 2727
Step 10: 2727 + 303 = 3030
Step 11: 3030 + 303 = 3333
Step 12: 3333 + 303 = 3636
Step 13: 3636 + 303 = 3939
Step 14: 3939 + 303 = 4242
Step 15: 4242 + 303 = 4545
Step 16: 4545 + 303 = 4848
Step 17: 4848 + 303 = 5151
Step 18: 5151 + 303 = 5454
Step 19: 5454 + 303 = 5757
Step 20: 5757 + 303 = 6060
Step 21: 6060 + 303 = 6363
Step 22: 6363 + 303 = 6666
Step 23: 6666 + 303 = 6969

So, 303*23 = 6969