Let's denote the sale price of the dress as \( d \) dollars. The regular price of the dress, which is 3 times the sale price, thus can be expressed as:
\[ \text{Regular Price} = 3d \]
Janine has enough money to buy 2 dresses at the regular price. Therefore, the total amount of money Janine has is:
\[ \text{Total Money} = 2 \times \text{Regular Price} = 2 \times 3d = 6d \]
Now, we want to find out how many dresses Janine can buy at the sale price of \( d \) dollars. To find this, we divide her total amount of money by the sale price:
\[ \text{Number of Dresses} = \frac{\text{Total Money}}{\text{Sale Price}} = \frac{6d}{d} \]
Simplifying the above expression, we get:
\[ \text{Number of Dresses} = 6 \]
Thus, Janine can buy \( \boxed{6} \) dresses at the sale price.