Alright, let's work through 6976 times 5677 step by step
6976 × 5677 = 5677 × (6976)
+ 5677 × 6 that results in 34062
+ 5677 × 70 producing 397390
+ 5677 × 900 producing 5109300
+ 5677 × 6000 giving us 34062000

= 39602752
