To find the price per inch of the 2-foot piece of string, we first need to convert feet to inches. Since there are 12 inches in a foot, a 2-foot piece of string is:
\[ 2 \text{ feet} \times 12 \text{ inches/foot} = 24 \text{ inches} \]
Next, we know that the cost of the 2-foot string is $1.68. To find the price per inch, we divide the total cost by the total number of inches:
\[ \text{Price per inch} = \frac{\text{Total cost}}{\text{Total inches}} = \frac{1.68}{24} \]
Now, we perform the division:
\[ \frac{1.68}{24} = 0.07 \]
Therefore, the price per inch of the string is \( \boxed{0.07} \) dollars, or 7 cents per inch.