Explanation

Observe that (4a − 2/a²)³ = 64a³ − 96 + 48/a³ − 8/a⁶, using (u−v)³ = u³ − 3u²v + 3uv² − v³. The given equation is exactly −(4a − 2/a²)³ − t³ = 0, so t³ = −(4a − 2/a²)³ and t = 2/a² − 4a. Then a²t + 4a³ = a²(2/a² − 4a) + 4a³ = 2 − 4a³ + 4a³ = 2. This is option (c).