Answer
4 seconds
Work Step by Step
Recall that the time constant for an RC circuit is $\tau = RC$
While we're given the total capacitance since there's only one capacitor, we still need to find the total resistance.
When the switch is closed, the resistors are in series and $R_{total} = \Sigma_i^nR_i = R_1+R_2+...+R_n$
$R_{total} = 2 \Omega + 2\Omega = 4\Omega$
$\therefore \tau = RC = (4\Omega)(1F) = 4 $ s
