Correct Answer  Option 2 : x < y
I. \(3{x^2} + 8x + 4 = 0\)
\( \Rightarrow 3{x^2} + 6x + 2x + 4 = 0\)
\( \Rightarrow 3x\left( {x + 2} \right) + 2\left( {x + 2} \right) = 0\)
\( \Rightarrow \left( {x + 2} \right)\left( {3x + 2} \right) = 0\)
∴ x = 2 or 2/3
II. \(4{y^2}  19y + 12 = 0\)
\( \Rightarrow 4{y^2}  16y  3y + 12 = 0\)
\( \Rightarrow 4y\left( {y  4} \right)  3\left( {y  4} \right) = 0\)
\( \Rightarrow \left( {y  4} \right)\left( {4y  3} \right) = 0\)
∴ y = 4 or 3/4
Comparison between x and y (via Tabulation):
Value of x

Value of y

Relation

2

4

x < y

2

3/4

x < y

2/3

4

x < y

2/3

3/4

x < y

∴ Clearly x < y