The value $1.5789$ that is calculated is the density of the probability mass at $x = 6$ with units mass/foot; it is not the probability that a randomly selected male has height exactly $6$ feet. To get a probability, you have to multiply the value of the probability density by a length. In other words, the probability that a randomly selected male has height between $5$ feet, $11\frac{1}{2}$ inches and $6$ feet, $\frac{1}{2}$ inches is approximately $1.5789 \times \frac{1}{12}$ (because the unit of height ($x$ axis) is a foot and thus the length in question is $1$ inch = $\frac{1}{12}$ foot). Note that the value of the probability that we thus obtain is an approximation, but a very good approximation in this instance. (To get an exact value, we would need to compute the value of an integral, but $1.5789/12 = 0.1315\ldots$ is good enough for gummint purposes).
As a practical matter, heights are often recorded to the nearest inch, and so when someone says a particular male is $6$ feet tall, people usually take it to mean that the person is between $5$'$11\frac{1}{2}$" and $6$'$\frac{1}{2}$" anyway. But in this sense of the phrase, the probability that a randomly chosen male is $6$ feet tall is $13.15\%$, not $157.89\%$.