1)The equipment you would use for carrying out a simple distillation at reduced pressure (i.e. under vacuum)

2)What could be the advantage of carrying out a distillation under vacuum as compared to atmospheric pressure?

1. You don't have a picture in your book/experiment manual that gives you this information?

2. Many compounds decompose at normal boiling points under atmospheric pressure but under reduced pressure the boiling point is much lower where decomposition doesn't occur.
Remember the boiling point of any material is the temperature at which the vapor pressure of the material is the same as atmospheric pressure. Therefore, water boils at 100 C because its vapor pressure at 100 C is 760 mm Hg which is normal atmospheric pressure. If you go to the top of Pikes Peak where the atmospheric pressure may be as low as 500 mm Hg or less, the boiling point of water is as low as 80-85 C.