Answer
The direction of rotation is clockwise.
Work Step by Step
Note that by convention, a clockwise rotation is negative.
We can use conservation of angular momentum to find the angular velocity after coupling:
$L_f = L_i$
$(I_1+I_2)~\omega_f = I_1~\omega_1+I_2~\omega_2$
$\omega_f =\frac{ I_1~\omega_1+I_2~\omega_2}{I_1+I_2}$
$\omega_f =\frac{(3.30~kg~m^2)(450~rev/min)+(6.60~kg~m^2)(-900~rev/min)}{3.30~kg~m^2+6.60~kg~m^2}$
$\omega_f = -450~rev/min$
Since the angular velocity after coupling is negative, the direction of rotation is clockwise.
