Let's denote the cost of an entrance ticket as \( x \). Since there are 4 friends, the total cost before the grip sock fees would be \( 4x \).
Each entrance ticket has an additional cost of $2 for grip socks, so for all 4 tickets, the total fee for the socks would be \( 4 \times 2 = 8 \) dollars.
Therefore, the total cost can be expressed as:
\[ 4x + 8 = 68 \]
To find \( 4x \), we will subtract the sock fee from the total cost:
\[ 4x = 68 - 8 \]
\[ 4x = 60 \]
Next, we solve for \( x \) by dividing both sides by 4:
\[ x = \frac{60}{4} \]
\[ x = 15 \]
Thus, the cost of an entrance ticket is \( \boxed{15} \).