The graph of the function f(x) = 2x^2 - kx + 18 touches the x-axis when the equation 2x^2 - kx + 18 = 0 has a real solution. For that to happen the following condition should be satisfied: `k^2 - 4*2*18 >= 0`
As the value of k for which the graph does not touch the x-axis is required `k^2 - 144 < 0`
=> `k^2 < 144`
=> `-12 < k < 12`
For k lying in the set (-12 , 12) the graph of the function f(x) = 2x^2 - kx + 18 does not touch the x-axis.