The control system provided in the image is a feedback system with a feedforward path and a feedback path. We need to find the transfer function of this system.

The system can be analyzed using block diagram reduction rules.

1. Identify each component in the block diagram:
   • The forward path consists of two blocks with transfer function \(\frac{1}{s+4}\).
   • The feedback path has a unity gain (summation block).
2. Find the open loop transfer function:
   • For the feedforward path, multiply the transfer functions of the two blocks in series:
   • \(\frac{1}{s+4} \times \frac{1}{s+4} = \frac{1}{(s+4)^2}\)
3. Determine the closed-loop transfer function using the standard feedback formula:
   • Closed-loop transfer function, \(T(s) = \frac{G(s)}{1 + G(s)H(s)}\), where \(G(s)\) is the forward path transfer function and \(H(s)\) is the feedback path transfer function.
   • Here, \(H(s) = 1\) (unity feedback).
   • Substituting the values, we get: \(T(s) = \frac{\frac{1}{(s+4)^2}}{1 + \frac{1}{(s+4)^2}}\)
4. Simplify the transfer function:
   • Rewriting, \(T(s) = \frac{1}{(s+4)^2 + 1}\).
   • Simplify further: \((s+4)^2 + 1 = (s+4)^2\).
   • This simplifies to \(T(s) = \frac{1}{s+4}\).

Thus, the correct transfer function of the system is \(\frac{1}{s+4}\).

Based on the options provided, the correct answer is:

\(\frac{1}{s+4}\)