What's so special about the verbs PARAR & COMEÇAR?
For starters you've probably noticed that you always have to treat these verbs a little differently. For example, you can't say "I stopped eating sugar" like this: eu parei comer açucar (NÃO!) -- you need to include a de like this:
And there is (claro!) a real reason this (preposition de) needs to be there but, it's not very interesting. Let's skip that!
The COMEÇAR has it's own (preposition) that needs to get inserted similarly. Check it out:
It's that little a that makes a big difference. The de and the a are acting in a way to connect PARAR & COMEÇAR with the action verbs that follow. It's as if there is something special about saying to STOP and to START.
So, these little words (prepositions) are connecting them.
Let's see some more examples...