$x[n]$ after sampling of $cos(16\pi t+\phi)$ at 12kHz
First of all, as you said the sampling rate is probably $12$ Hz, rather than $12$ kHz, and perhaps they want to demonstrate an aliasing example.

Given a bandlimited continuous-time periodic signal 
$$x(t) = \cos(16\pi t + \phi)$$ 
the samples taken at the rate $F_s = 12$ Hz will be denoted as $x[n]$ and will be obtained by via $x[n] = x(t_n)$ with $t_n = n T_s = n/Fs$ :

$$x[n] = \cos( 16 \pi \frac{1}{12} n + \phi) = \cos(\frac{4 \pi}{3} n + \phi)$$

$x[n]$ is a discrete-time periodic sequence with frequency $w_0 = \frac{4\pi}{3}$, however, in the discrete-time case we are interested in the range of frequencies that fall in $ [-\pi,\pi)$, and therefore this signal's frequency will be cast as:

$$ x[n] = \cos(\frac{4 \pi}{3} n + \phi) = \cos(\frac{2 \pi}{3} n + \phi)$$

which indicates that the original continuous-time frequency of $8$ Hz is lost, and a new aliased frequency of $4$ Hz is attained...