Answer
$\tau = 8 \times 10^{-3}~s$
Work Step by Step
The equivalent capacitance of $2~\mu F$ and $2~\mu F$ in parallel is $C = 4~\mu F$
The equivalent resistance of $1~k \Omega$ and $1~k \Omega$ in series is $R = 2~k \Omega$
We can find the time constant $\tau$:
$\tau = R~C$
$\tau = (2 \times 10^3~\Omega)(4 \times 10^{-6}~F)$
$\tau = 8 \times 10^{-3}~s$
