That means to study or ruminate, ponder, to think about carefully, consider, again and again, with great care, for an exceedingly long period of time, until the thing you are mulling about has taken care of itself and you are conveniently off the hook. Again.
It also means to mess up or make a failure of.
Germany mulls joining European Persian Gulf naval mission – Pressure is growing on the German government to lend its military weight to a potential European naval mission in the Persian Gulf. The UK government floated the idea of a joint European operation last Monday.
“Hardly any other country is as dependent on the freedom of international shipping as export champions Germany.”