Alright, let's work through 8637 times 977 step by step
8637 × 977 = 977 × (8637)
+ 977 × 7 giving us 6839
+ 977 × 30 which equals 29310
+ 977 × 600 that equals 586200
+ 977 × 8000 yielding 7816000

= 8438349
