Here's why:

1. Alpha Centauri A and B: These are the closest stars to our Sun, forming a binary star system.

2. Proxima Centauri: This is a red dwarf star that's part of the Alpha Centauri system, but slightly further away than A and B.

3. Barnard's Star: This is a red dwarf star slightly further out than Proxima Centauri.

So, the order of nearest stars is:

1. Alpha Centauri A & B

2. Proxima Centauri

3. Barnard's Star

4. Proxima Centauri