Alright, let's work through 6353 times 6478 step by step
6353 × 6478 = 6478 × (6353)
+ 6478 × 3 that equals 19434
+ 6478 × 50 that results in 323900
+ 6478 × 300 giving us 1943400
+ 6478 × 6000 resulting in 38868000

= 41154734
