Hello!
To answer your first question, no, that isn't in standard form.
For something to be in standard form, x can't be negative, both x and y need to be on the left side, and there can't be fractions.
Taking the three rules, let's make that equation have no fractions. In order to remove the fractions, you multiply everything by 3.
2/3x - 1/3y = 2
2x - y = 6
Let's go over the rules again to make sure:
X isn't negative - correct.
x and y is on the left side - correct
No fractions - correct.
Now that it passed all the rules, 2x - y = 6 would be your correct standard form equation.
Hope I helped (: