We start by letting \( x \) represent the total number of free throws Nayeli attempted. According to the problem, she misses 20% of those attempts.
To express this mathematically, we can write:
\[ \text{Missed free throws} = 0.2x \]
We know that she missed 60 free throws, so we can set up the equation:
\[ 0.2x = 60 \]
Next, to solve for \( x \), we will divide both sides of the equation by 0.2:
\[ x = \frac{60}{0.2} \]
Now, we perform the division:
\[ x = 60 \div 0.2 = 60 \div \frac{2}{10} = 60 \times \frac{10}{2} = 60 \times 5 = 300 \]
Thus, the total number of free throws Nayeli attempted is
\[ \boxed{300} \]