Would using 'bemászik' instead of 'mászik be' also be correct, and if not what is the difference?
The difference is a matter of grammatical aspect: splitting the coverb and verb means the action is happening right now ('is climbing' or 'is crawling'). As opposed to, say, 'a pók mindig bemászik a cipőmbe' (the spider always climbs into my shoe').
Wow, thanks, I learn Hungarian for quite a long time already, but nobody told me that!
Not a spider crawls into the shoe but a bug. Not accepted. Why?