Billy slept 6 hours the first night. He then slept 6+2=<<6+2=8>>8 hours the second night.
Billy then slept 8/2=<<8/2=4>>4 hours the third night.
Finally, Billy slept 4*3=<<4*3=12>>12 hours the fourth night.
In total, Billy slept 6+8+4+12=<<6+8+4+12=30>>30 hours.
#### 30