Question

What is the value of x, given PQ || BC?

Answer 1

This is clearly a job for the Thales theorem, my friend :)

Answer 2

How do you do Thales theorem?

Answer 3

6/12=x/26

Answer 4

therefore its 13

Answer 5

Thales therem says, that all those are proportional.
Applying it to your problem:
\[\frac{ AB }{AP }=\frac{ AC }{ AQ }=\frac{ BC }{ PQ }\]