(b) 0.06 A
In a series circuit, the same current flows through every component. So the current through the 6W bulb is also 0.06 A.
The key principle here is that in a series combination, current remains the same throughout the circuit, regardless of the resistance or power rating of each component. The textbook (Activity 11.4, Section 11.6.1) clearly states: "the current is the same in every part of the circuit." Students often confuse series and parallel — in parallel, current divides; in series, it does not.