You know that the graphy of f(x) is trending upward with slopw 2 at x = 6, and it trends downward with slope -3 at x=8. So if the function is continuous that means either (a) there is a point some place between x=6 and x= 8 where the slope is equal to 0, or (b) the function is "jagged" and takes a sharp turn someplace between x=6 and x=8. In either case the function must hit a local maximum in the interval betwen x=6 and x=8.

I think you would find it helpful to sketch some example of graphs that have these slopes, and you'll see how if the slope goes from positive to negative there must be a local maximum in between.