Alright, let's work through 1189 times 5556 step by step
1189 × 5556 = 5556 × (1189)
+ 5556 × 9 that results in 50004
+ 5556 × 80 resulting in 444480
+ 5556 × 100 what gives us 555600
+ 5556 × 1000 resulting in 5556000

= 6606084
