Can a 6 volt battery light up a 4 watt bulb?

More voltage than required will light something such as a bulb.

However, you have to consider such things as bulb longevity. Anything over 12 volts will illuminate a 12 volt bulb. If it's connected to an engine alternator and not a pure clean 12 volt power supply, ideally 13.5-14 volts is the voltage you're looking for to power this bulb.

16 volts will work, but it may prematurely burn the bulb out.

That is, unless it is an LED. Even overpowered they will continue to burn bright, but not burn out, but it won't last as long as if it were connected to a true 12 volt supply voltage. But in the end, even an overpowered LED will last longer than an overpowered 12V incandescent bulb.

It will definitely burn out prematurely if a higher than design intent voltage is supplied, however the hours. minutes, seconds lost may not be as high as people may assume them to be, from 12v to 16v is not such a jump especially in light of most automotive applications having output voltages up to 14.8v a car battery typically has 6 x 2.2v cells making 13.2v