The formula for the circumference \( C \) of a circle is given by:
\[ C = 2\pi r \]
where \( r \) is the radius. Given the radius \( r = 38 \) inches and using \( \pi \approx 3.14 \), we can calculate the circumference:
\[ C = 2 \times 3.14 \times 38 \]
Calculating that:
\[ C = 6.28 \times 38 \]
Now, performing the multiplication:
\[ C = 238.64 \]
Therefore, the approximate circumference of the circle is \( \boxed{238.64} \) inches.