Alright, let's work through 6353 times 3677 step by step
6353 × 3677 = 3677 × (6353)
+ 3677 × 3 what gives us 11031
+ 3677 × 50 that results in 183850
+ 3677 × 300 that is equal 1103100
+ 3677 × 6000 producing 22062000

= 23359981
