Let the total number of students in Regan's class be \( x \). Since 3 students didn't turn in permission slips, the number of students going on the trip is \( x - 3 \).
Regan is stocking 2 bottles of water for each student going, which means the total number of bottles stocked is:
\[ 2(x - 3) \]
We know that Regan stocked 46 bottles of water, so we can set up the equation:
\[ 2(x - 3) = 46 \]
Now, we will solve for \( x \):
- Divide both sides by 2:
\[ x - 3 = 23 \]
- Add 3 to both sides:
\[ x = 26 \]
Thus, the total number of students in Regan's class is \( \boxed{26} \).