She gets paid $12 per hour.
Let x be the amount she gets paid per hour. Working 40 hours would then be represented by 40x.
Anything over 40 hours earns her 1.5 her normal rate, or 1.5x. Since she works 52 hours, this means 52-40=12 hours of overtime at 1.5x:
12(1.5x) = 18x
Together, she earned 696:
40x+18x = 696
Combining like terms,
58x = 696
Divide both sides by 58:
58x/58 = 696/58
x = 12