Julia baked one less than 5 cakes per day, or 5-1=<<5-1=4>>4 cakes per day.
For 6 days, Julia baked 4 cakes per day, for a total of 4*6=<<4*6=24>>24 cakes.
Over 6 days, every other day, Clifford sneaks into Julia's house and eats one of Julia's cakes resulting in disappearance of 6/2=<<6/2=3>>3 cakes.
At the end of 6 days, Julia has 24-3=<<24-3=21>>21 cakes remaining.
#### 21