Alright, let's work through 6337 times 8623 step by step
6337 × 8623 = 8623 × (6337)
+ 8623 × 7 that results in 60361
+ 8623 × 30 that is equal 258690
+ 8623 × 300 giving us 2586900
+ 8623 × 6000 that is equal 51738000

= 54643951
