Answer
$k = 5.48~N/m$
Work Step by Step
We first find the period as:
$T = \frac{time}{cycles}$
$T = \frac{12.0~s}{10~oscillations}$
$T = 1.20~s$
We then find the spring constant as:
$T = 2\pi~\sqrt{\frac{m}{k}}$
$k = \frac{(2\pi)^2~m}{T^2}$
$k = \frac{(2\pi)^2~(0.200~kg)}{(1.20~s)^2}$
$k = 5.48~N/m$