Alright, let's work through 7383 times 7688 step by step
7383 × 7688 = 7688 × (7383)
+ 7688 × 3 giving us 23064
+ 7688 × 80 resulting in 615040
+ 7688 × 300 giving us 2306400
+ 7688 × 7000 resulting in 53816000

= 56760504
