The diameters of washers produced by a machine follow a Normal distribution with standard deviation 0.1 mm and unknown mean $\mu$. The mean is to be set so that the probability that a diameter exceeds 2.0 mm is 0.03.

The tail probability above 2.0 mm is 0.03, so the probability below it is $1 - 0.03 = 0.97$.

A Normal table gives the value of the standard Normal variable whose cumulative probability is 0.97, and reading it off gives $z = 1.881$.

This is the number the standardised diameter $\dfrac{2 - \mu}{0.1}$ must equal, and everything else in the question follows from it.