There are two ways to do it, with and without algebra. I'll do it both ways:

FIRST WAY (WITHOUT ALGEBRA):

Start at the end and go backwards.

There were 8 lollies left. 

Therefore since 8 were left after taking three quarters, the 8 must have been
the one quarter that was left, so there were 4 times 8 or 32 lollies before.

Then before that they ate half a bag, so those 32 must have been half of what
they started with, so they started with 64 lollies.

SECOND WAY (WITH ALGEBRA)

There were N lollies to begin with 

So there was half a bag or  left

Since they ate  the day before, they ate , so we subtract that from what they had left.
So after that, the had this many left:

  

Multiplying those two fractions

 

So we set that equal to 8



Multiply through by LCD = 8





Same answer as when we didn't use algebra and worked backwards.

Edwin