Translation:Older people do not like to drive with a bicycle helmet.
You use "at køre" with anything that drives on wheels. That includes skateboards and roller skates.
(Just FYI, in case you folks are learning other Scandinavian languages also; This "rule" applies only to Danish. In Swedish and Norwegian, you cannot use the work 'köre'/'kjøre' when talking about bicycling, rollerblading etc., but you can use it for cars, tractors and most motorised vehicles, even a motorbike.)
I swore I would not waste any more time making comments on the inane "correct" versions that Duolingo offers but,,, "drive with a bicycle helmet" is not English because in English you do not "drive" a bike. You "ride" a bike or you cycle. But hey, I suppose for Duolingo this is not an English course so it doesn't matter how bad the English is.