What is the output in Figure 3-19(a) if the input voltage is increased to a peak value of 20 v?
The peaks will increase because real zeners are not "ideal" and have an internal resistance that causes a greater volt drop when conducting more current (due to the increased input voltage).

The slopes will approximately double because the input waveform has doubled in magnitude.


  Or the zener diodes will breakdown (get damaged)?


An unfortunate choice of words - a zener is said to breakdown when the reverse voltage exceeds the "breakdown" voltage. It doesn't mean it will break-down (like a car) and there isn't enough information in the question to ascertain if either zener will fail when the input voltage doubles.