To solve the system of equations:

Step 1: Write the equations

[ \begin{cases} 2x + 3y = 12 \quad \text{(Equation 1)} \ 4x - 5y = 2 \quad \text{(Equation 2)} \end{cases} ]

Step 2: Eliminate (x)

Multiply Equation 1 by 2 to make the coefficients of (x) equal:
[4x + 6y = 24 \quad \text{(Equation 3)}]

Subtract Equation 2 from Equation 3:
[ (4x + 6y) - (4x - 5y) = 24 - 2 \ 11y = 22 \ y = 2 ]

Step 3: Find (x)

Substitute (y=2) into Equation 1:
[2x + 3(2) = 12 \ 2x + 6 = 12 \ 2x = 6 \ x = 3 ]

Answer: (x=3, y=2)

(\boxed{(3,2)})

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