To determine the total energy of x(t) = 12 Sinc (6t), we need to calculate the integral of the squared magnitude of the function over its entire domain.

The magnitude of the function is given by |x(t)| = 12 |Sinc (6t)|.

To calculate the total energy, we need to integrate the square of the magnitude over the domain of t.

∫ [|x(t)|^2] dt = ∫ [12^2 |Sinc (6t)|^2] dt

Since Sinc (6t) is a periodic function with a period of π/6, we can integrate over one period and then multiply by the total number of periods.

Let's integrate over one period, from -π/12 to π/12:

∫ [|x(t)|^2] dt = 12^2 ∫ [Sinc (6t)]^2 dt

Using the identity Sinc^2 (x) = (1/2) [1 - Cos(2x)], we can simplify the integral:

∫ [|x(t)|^2] dt = 12^2 ∫ (1/2) [1 - Cos(2*6t)] dt
= 72 ∫ [1 - Cos(12t)] dt
= 72 [t - (1/12) Sin(12t)] + C

Now, we can calculate the total energy by multiplying the integral over one period by the total number of periods.

Since the period of Sinc (6t) is π/6, the total number of periods in the domain of t is (2π)/(π/6) = 12.

Total energy = 72 * 12 [t - (1/12) Sin(12t)] | from -π/12 to π/12
= 72 * 12 [(π/12) - (1/12) Sin(π)]
= 72 * 12 (π/12)
= 72 π

Therefore, the total energy of x(t) = 12 Sinc (6t) is 72 π.