A small solid sphere of density d is dropped into a tall cylinder...

Let the volume of the sphere be $V$.

The true weight of the sphere is given by $W = V d g$.

The buoyant force acting on the sphere is $F_B = V \left(\dfrac{d}{3}\right) g = \dfrac{V d g}{3} = \dfrac{W}{3}$.

When the sphere reaches a constant terminal velocity, the net force acting on it is zero. The downward weight is balanced by the upward buoyant force and the viscous drag force $F_v$.

$W = F_B + F_v$

$F_v = W - F_B$

$F_v = W - \dfrac{W}{3} = \dfrac{2W}{3}$

Answer: $\dfrac{2W}{3}$