Use Chebyshev Inequality to estimate the probability that in any one day of a business that earns a mean of 100 dollars a day with a standard deviation of 28.87 dollars, that business will make either less than 60 dollars or more than 140 dollars.
$$\mu = 100,\quad \theta=28.87$$
$$P(|X-\mu| \ge d) \le \frac{\theta^2}{d^2}$$
$$X\sim N(100, 28.87^2)$$
$$\theta = 28.87\text{ and }d = 40$$
I understand everything up until $d = 40$. How does one obtain $d$?
You have $$ |X-\mu| \ge d. $$ That's the same as saying $$ X-\mu \ge d\text{ or }X-\mu\le-d, $$ ("or", not "and") which is in turn equivalent to $$ X\ge\mu+d\text{ or }X\le\mu-d. $$ So you have $\mu+d=140$ and $\mu-d=60$ and $\mu=100$.
If $d=40$ and $\theta=28.87$ then $\dfrac{\theta^2}{d^2}=\text{a certain number}$. That's all you need to answer your question.
But if you know it's normally distributed, you can get far more accurate values for this probability.