It's quantitative because you can count the number of leaves. Any time there is a number involved, it is quantitative. A qualitative variable is something like "names of a person" in which no numbers are involved
Because we're counting the whole number of leaves, this means the quantitative variable is also discrete. Discrete is a fancy way of saying "there are a finite number of items". In contrast, continuous means that there are infinitely many values because we can continually divide up the number line.
In summary, the answers are "quantitative" and "discrete"
