Alright, let's work through 6377 times 5915 step by step
6377 × 5915 = 5915 × (6377)
+ 5915 × 7 that is equal 41405
+ 5915 × 70 that equals 414050
+ 5915 × 300 giving us 1774500
+ 5915 × 6000 resulting in 35490000

= 37719955
