The program I was trying to install took a 2.0 or higher net frame work.
No such program exists. If a program was created for .NET 2.0, you must have 2.0 installed; 4.0 will not do. However, you will need 4.0 installed to run 4.0 applications; but 4.0 applications will not run applications created for previous versions of .NET.
Just consider the different major versions as entirely separate products; 1.1, 2.0, 3.0, 3.5, and 4 are the versions you would likely encounter. Some people prefer to install all of them at once; there is no performance hit and you are "prepared" for the eventuality that you get a program that does require it, at which point you would have needed to install it anyway.