(I'm going to assume you meant f(x) = 6x^2 - 28x + 16)
To find the x-Intercepts, simply find the roots of the equation 6x^2-28x+16=0. There are several ways one can do this. The way I do it is as follows:
6x^2 - 4x - 24x + 16 = 0 (Splitting the x term up so that the two add to equal -28 and multiply to give 6*16=96)
2x(3x-2) - 8(3x-2) = 0
(2x-8)(3x-2) = 0
Hence the roots are:
and therefore the 2 x-Intercepts are (4,0) and (2/3,0).