solving minimum voltage to turn on a diode
The book is using 0.7 volts for Vd. Here is a way to solve this circuit.

First off you can simplify by combining the 6 and 12 Ohm resistors.







simulate this circuit &ndash; Schematic created using CircuitLab

Which becomes:







simulate this circuit

Then you can use Norton's theorem on the Voltage Source and the 20 Ohm resistor:







simulate this circuit

Combine parallel resistors:







simulate this circuit

Norton again:







simulate this circuit

Now you can write a simple equation:

2V = 6.667i +.7 + 4I