I couldn't understand any equations you wrote. So, will start afresh.
Assuming Deb had x toys and Ananya had y toys,
x + y = 20 ==>
y = 20 - x
(x - 3) (y - 4)= 42 ==>
(x - 3) (20 - x -4) = 42 ==>
(x - 3) (16 - x) = 42 ==>
-x^2 +16x + 3x - 48 = 42 ==>
-x^2 +19x - 48 = 42