What are anti and gauche conformations?
In the most stable conformation, the two methyl groups lie as far apart from each other as possible with a dihedral angle of 180 degrees. This particular staggered conformation is called anti. The other staggered conformation has a Me-Me dihedral angle of 60 degrees and is called gauche.
What is anti staggered conformation?
Anti-staggered: A staggered conformation in which the two largest groups are anti (i.e., have a 180o dihedral angle). Anti-staggered conformation of butane. Sawhorse projection. Newman projection. Related terms: Syn, periplanar, syn-periplanar, anti-periplanar, gauche, eclipsed, conformational isomer, conformer.

Why is Anticonformation more stable?
As rotation continues, the molecule comes to the anti conformation, which is the most stable since the substituents are staggered and the methyl groups are as far away from each other as possible.
Why is anti conformation more stable than gauche?
The gauche form is less stable than the anti form due to steric hindrance between the two methyl groups but still is more stable than the eclipsed formations.
How do you know if it is anti or syn?

When both atoms/groups add to the same face it’s considered syn addition. When they add to opposite faces it’s considered anti addition. The difference between the two is determined by which atom the group added to (Mark vs Anti-Mark) or to which SIDE it adds (syn vs anti).
Which is more stable syn or anti?
The steric argument notes that the syn transition state is an eclipsed conformation. The anti state is in the more energetically stable staggered conformation. Since the rate of a reaction is inversely proportional to the stability of the transition state, the anti route should be much more favorable.
Which is more stable anti or gauche?
Which Newman projection is more stable?
6. Newman projection of butane in the “more-stable eclipsed” conformation. At 180 degrees, the molecule is staggered again and has settled into a regular, zig-zag, letter Z shape. There is no torsional strain, so this is one of the more stable shapes that the molecule can adopt.