It is common to combine er, hier, and daar with prepositions into one word, so I think it is better to realise that and try to recognise those words, than to start memorising phrases. To give you an idea how common these kind of words are, have a look at the possibilities in this list: https://onzetaal.nl/taaladvies/advies/er-voorzetsel-werkwoord#lijst
If followed by a specific object, you'd use "met dit". If left unspecified, you need "ermee" or "hiermee". Ermee and hiermee always refer to something mentioned before.
"Wat doet hij met dit ding?"=What is he doing with this thing? "Wat is dit ding, en wat doet hij hiermee?"= What is this thing, and what is he doing with it?
The usage here follows a pretty striaghtforward near/far dichotomy.
Hier = this (here)
Daar = that (there)
So with that would be daarmee.
Ermee is the unstressed version, so it refers to whatever is already understood as the object in question, regardless of how it would be translated to English.