For the below question:




Why did he take the absolute value for the threshold voltage as shown below?





As far as I understand we plug in the values with their signs. Am I right?

 

Yes, but there is a bit of a catch here. Check where the voltages are being referenced to.

 

It might help to draw the FET the right way round - we normally put positive voltages up top. Then you might see how the voltages relate.
Interesting symbol though. P channel MOSFET with no body. There are such things in the wild but they are not common.