How to simplify the expression qr+2q^2-3qr-r^2-6q^2

Let's make sure we organize everything.

qr
2q^2
-3qr
-r^2
-6q^2

Now combine like terms.
qr - 3qr = -2qr
2q^2 - 6q^2 = -4q^2
-r^2 is by itself.

So, your

-4q^2-2qr-r^2