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2y-6>-3
Swap sides so that all variable terms are on the left hand side. This changes the sign direction.
2y>-3+6
Add 6 to both sides.
2y>3
Add -3 and 6 to get 3.
y>\frac{3}{2}
Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.