Assumptions when designing an amplifier
The 0.4 V across the Thevenin resistor (R1//R2) is a somewhat arbitrary design choice based on the emitter voltage. It is the voltage drop caused by the Ib of the transistor because it loads the voltage divider made by R1 and R2.

Choosing more than 0.4 V would result in higher values for R1 and R2 resulting in a larger voltage drop caused by Ib resulting in ending up with a different emitter voltage than the 4 V we wanted.

And likewise a lower value would result in less voltage drop.

I think they just used 10% of the emitter voltage (4V) as the value. That makes sense as the 0.6 V drop from  \$V_{be}\$ is relatively constant. And if the emitter voltage was lower, 1 V for example, you would want the voltage drop due to \$I_b\$ to be smaller as well to prevent ending up too far away from the initial calculations.