"How many lörtsy do you want?"
Translation:Montako lörtsyä haluatte?
"Moni" is in nominative case so it's used when its noun phrase is in nominative case, and "monta" is in partitive case so it's used when its noun phrase is in partitive case. Since this noun phrase is the object of an irresultative verb, partitive case is required.
If I'm not mistaken, paljonko works only with uncountable nouns and requires the partitive case, whereas montako is used with countable:
- Paljonko kakkua meillä on? – how much cake do we have?
- Montako palaa kakkua meillä on? – how many pieces of cake do we have?
- Montako kakkua meillä on? – how many cakes do we have?
Edit: ok, cake was not the best example here because you can consider cake both as countable and uncountable. The above does not work with lörtsy because it's a pastry which is not supposed to be divided.
In that sense it's more like auto, you can't really ask e.g. paljonko autoa ostat ("how much car are you buying"), rather you'd ask montako autoa ostat ("how many cars are you buying").
Please ask for more clarification if you feel so, hope it still helps...