Alright, let's work through 3417 times 9966 step by step
3417 × 9966 = 9966 × (3417)
+ 9966 × 7 producing 69762
+ 9966 × 10 that is equal 99660
+ 9966 × 400 which equals 3986400
+ 9966 × 3000 which equals 29898000

= 34053822
