Right choice is (a) Stable but not causal
The best explanation: \(∑_{k=-∞}^∞ h(k) = ∑_{k=-3}^∞ u(k+3) + ∑_{k=2}^∞ u(k-2) – 2∑_{k=7}^∞ u(k-7)\)
= \(∑_{k=-3}^6 1 + ∑_{k=2}^6 1\)
= 10 + 5
= 15 < ∞
For bounded input, we are getting bounded output. So system is stable.
The response depends on future value of input signal i.e. u (n+3). So, the system is not causal.