Step 1 :Given the function \(f(x, y)=6 x^{2}-y\) and the point \((-6,2)\).
Step 2 :Substitute \(x = -6\) and \(y = 2\) into the function.
Step 3 :Calculate the value of the function: \(f(-6, 2) = 6*(-6)^{2}-2 = 214\).
Step 4 :Final Answer: The value of the function \(f(x, y)=6 x^{2}-y\) at the point \((-6,2)\) is \(\boxed{214}\).