Let the length of the shorter piece be denoted as \( x \) feet. According to the problem, the longer piece is 4 feet more than 2 times the length of the shorter piece. Therefore, the length of the longer piece can be expressed as:
\[ 2x + 4 \]
The total length of the board is 25 feet. This gives us the equation:
\[ x + (2x + 4) = 25 \]
Now, simplify the equation:
\[ x + 2x + 4 = 25 \]
Combine like terms:
\[ 3x + 4 = 25 \]
Next, subtract 4 from both sides:
\[ 3x = 21 \]
Now, divide both sides by 3 to solve for \( x \):
\[ x = 7 \]
Thus, the length of the second, shorter piece of the board is:
\[ \boxed{7} \text{ feet.} \]
To check our work, we can find the length of the longer piece:
\[ 2x + 4 = 2(7) + 4 = 14 + 4 = 18 \text{ feet.} \]
Now, let's verify that the total length is 25 feet:
\[ 7 + 18 = 25 \text{ feet.} \]
Everything checks out, so the length of the second, shorter piece is indeed \( \boxed{7} \) feet.