I just want to say your skills at paint are somewhat terrifying. But getting on subject...
a nice way to do this is tree diagrams...
first draw all the combinations when going from Q to B to R back to Q
So there are 6 combinations that wayCode:Q / R--- Q / \ / Q Q-----B \ Q \ / R---Q \ Q
Now draw the number of combinations from Q to R to B back to Q
There are 6 combinations this way...Code:B---Q / R---B---Q / B---Q / / Q-----R \ \ \ B---Q R---B---Q \ B---Q
altogether that makes 12