The book is assuming you have two wye systems, 120/208 3Ø and 277/480 3Ø, and that you are measuring from one phase, say A, on one system, and another phase, say B, on the other system.
The book is also assuming that there is one supply from the PoCo that is connected to both of the two system transformers, and the transformers have the same type of primaries. That results in the 120V AØ being almost exactly in step with the 277V AØ.
Measuring voltage from 120V AØ to 277V BØ results in 380 Volts.
Al
