Halftone value images "simulate" a full-area coloring with the help of tiny dots of variable size which the observer's eye cannot discriminate anymore from a certain distance. This is the way newspapers, magazines and posters etc. are usually printed. Just take a close-up look at one of those, maybe even with magnifying glasses, and you'll see the dots.
Now, if the instructions are: "Maximum halftone value of 15%", then to me, that would mean that in any area of the image you want to print, no more than 15% of the paper should be covered by toner. That means that e.g. in an area of 10 x 10 millimeters, the dots' covered area cannot exceed 15 mm^2, that's approximately 15 dots with radius 0.3 mm, or approx. 5 dots of 1 mm radius. How this can be achieved, depends on the technology you're using. It will depend on how large the interval between dots will be (= the number of dots per inch, DPI) and what minimum and maximum size they can have with that printer. What "blackness" or color coverage you can achieve with this limitation, also depends on from how far you are going to look at the image.