Step 1 :Given the system of equations: \[\left\{\begin{array}{l} 4 x+y=8 \\ 6 x-9 y=12 \end{array}\right.\]
Step 2 :Express y in terms of x from the first equation: \(y = 8 - 4x\)
Step 3 :Substitute this expression into the second equation in place of y: \(6x - 9(8 - 4x) = 12\)
Step 4 :Simplify the equation to get the final answer: \(\boxed{42x - 72 = 12}\)