The correct answer is: C. Mixed phase
An FIR system is a linear time-invariant (LTI) system with a finite impulse response (FIR). The system function of an FIR system is given by
$$H(z) = \sum_{n=0}^{N-1} h[n] z^{-n}$$
where $h[n]$ is the impulse response of the system and $N$ is the number of taps in the impulse response.
The phase of an FIR system is given by
$$\phi(e^{j\omega}) = -\sum_{n=0}^{N-1} n \omega h[n]$$
where $\omega$ is the angular frequency.
An FIR system is said to be minimum phase if its phase is minimum over all possible FIR systems with the same magnitude response. An FIR system is said to be maximum phase if its phase is maximum over all possible FIR systems with the same magnitude response. An FIR system is said to be mixed phase if its phase is neither minimum nor maximum.
In this case, the system function is given by
$$H(z) = 1 + \frac{7}{2} z^{-1} + \frac{3}{z} z^{-2}$$
The phase of the system is given by
$$\phi(e^{j\omega}) = -\omega – \frac{7}{2} \sin(\omega) – \frac{3}{2} \cos(\omega)$$
The phase of the system is not constant, so the system is not minimum phase or maximum phase. Therefore, the system is mixed phase.