Sean has worked 66 hours over the last 10 days without a day off. he worked either a 6 hour day or an 8 hour day. during the 10 day period, how many days did sean work an 8 hour day?

He worked an 8 hour day 3 days.

Let x be the number of 8 hour days he works.  Then 10-x is the number of 6 hour days he works.

8x + 6(10-x) = 66

Using the distributive property,
8x + 6*10 - 6*x = 66
8x + 60 - 6x = 66

Combining like terms,
2x + 60 = 66

Subtract 60 from both sides:
2x + 60 - 60 = 66 - 60
2x = 6

Divide both sides by 2:
2x/2 = 6/2
x = 3

There were 3 days he worked 8 hours.