still not getting the clue.

Question

I can't seem to get it right. No me queda mucho dinero ________ tengo para dos cervezas más. How
 come this should be 'pero'. I thought it was a substitute. First clause
 is negative and replaced by another, positive clause, hence I thought 
'sino que'. Can one please point me to the critical part that would make
 me understand the difference? I feel so dumb.Thank you in advance!

Answer

After looking further, sino is used where the first (negative) is incorrect/false. More than just negative. It needs to be corrected to a true statement. Whereas when the negative clause is true in itself (no tengo mucho dinero), it does not need to be corrected, and thus pero suffices.
Is that getting close?

Answer

Hola Robert,
The negative sentences are the hardest in this case because they can use both "pero" and "sino" and the translation is still the same in English. We have, by the end of the lesson" a little explanation about what each of them conveys. 
With "pero" we are "adding" a new idea to the first statement; with sino we are "giving a substitute". 
For example, using the sentence you mentioned before:
"No me queda mucho dinero PERO tengo para dos cervezas más."I don't have much money left but I have [enough] for two more beers.
Here we are "adding" something new: the fact that I still have a bit of money.
Other examples with negative sentences could be:

No es guapo pero es muy simpático. (adding something new) He is not handsome but he is very nice.
No es guapo sino feo. (substituting, not adding) He is not handsome but ugly.
Ella no puede venir hoy pero no nos importa. (adding) She can't come today but we don't mind.
Ella no puede venir hoy sino mañana. (substituting) She can't come today but tomorrow.

I hope this is now a bit more clear.
Inma