Could you explain why that's not possible to say "Je lui parle en peu anglais"?

I don't know the writing exercise or the the specific sentence you refer to. Maybe this helps.

Je parle un peu anglais. -- I speak a little English. Je lui parle en anglais. -- I talk to him/her in English.

I'm referring to the writing exercise above, specifically this phrase: "...et je parle un peu anglais avec lui." I entered "Je lui parle en peu anglais" but it was marked as incorrect.

It is un peu. Also note that "to speak with" is parler avec qq. "To speak to" would be parler à qq.

The difference between "speak to" and "speak with" is basically just British English v American English. As far as I know there's no real difference between "parler à" and "parler avec" either.

Thanks!

In French there is a difference in nuance, though. Parler avec is stressing the fact that there is an exchange, i.e., the other person responds and a kind of discussion results. Parler à doesn't have this emphasis.

@Alan: I googled the English usage of "speak to" and "speak with". Apparently things aren't that clear cut. Some people see a difference in usage and meaning similar to French. But it seems more of splitting hairs in English than it is in French.

@Chris: If you ask someone to explain the difference between the two, they may well give an explanation like that - after all it seems logical. However it may not reflect actual usage. Does anyone actually bother to make this distinction in their own speech? I suspect that some people will consistently say "speak to" and others will say "speak with", and the same may apply in French. 

According to the Académie francaise there's no difference:

3.  Parler à, avec, adresser la parole à ; avoir un entretien, converser avec.