Final answer:
Direct calculation of y[4] for a unit sequence applied to a system given by the transfer function H(z) is not feasible without the complete time-domain response, which involves inverse z-transform and possibly partial fraction decomposition.
Step-by-step explanation:
When the system with the transfer function H(z) = z/(z²+z+0.24) is applied to a unit sequence u[n], the response at a given time can be computed using the z-transform properties and inverse z-transform techniques to find the corresponding time-domain sequence y[n].
However, finding y[4] directly from the transfer function without additional context or calculation steps, such as partial fraction decomposition and inverse z-transform, is not feasible as it requires the complete time-domain response. The full solution would involve transforming the transfer function back to the time-domain response using inverse z-transform methods and then determining the value of y[n] at n=4.