For this type of problem, it's probably easiest to draw a table like this:
Original Drawing
Our expression is composed of three factors, (x−3), (x−4), and (x−8). These three factors together with their product serve as the top row heading for the table. The most left-hand column shows different possibilities for x, The next column to the right of this shows whether the value of x−3 will be negative (-), zero (0), or positive (+) and the last column shows us if the product of the three factors is negative, zero, or positive.
Reading the first row below the heading we can see that when x is less than 3, x−3 is negative, x−4 is negative, and x−8 is negative, so the product of these three factors is also negative, since a negative times a negative times a negative is negative.
Looking at the table, we can see when the product of the factors is less than or equal to zero. This is when
x≤3, and 4≤x≤8.