This says, if you know ~Q and P -> Q then you can say ~P.
A simple example of modus-tollens is
\matrix{ 1. \hfill & \lnot Q \hfill & \hbox{Premise} \hfill \cr 2. \hfill & P ⊃ Q \hfill & \hbox{Premise} \hfill \cr 3. \hfill & \lnot P \hfill & \hbox{Modus tollens (1, 2)} \hfill \cr}
An invalid modus-tollens
\matrix{ 1. \hfill & Q \hfill & \hbox{Premise} \hfill \cr 2. \hfill & P ⊃ Q \hfill & \hbox{Premise} \hfill \cr 3. \hfill & \lnot P \hfill & \hbox{INVALID Modus tollens (1, 2)} \hfill \cr}
For example,
You water the garden, the garden get wet -> 1
the garden is not wet -> 2
You not watered the garden -> Modus tollens (1, 2)
Let’s verify the other way round,
\matrix{ 1. \hfill & \lnot P \hfill & \hbox{Premise} \hfill \cr 2. \hfill & P ⊃ Q \hfill & \hbox{Premise} \hfill \cr 3. \hfill & \lnot Q \hfill & \hbox{INVALID Modus tollens (1, 2)} \hfill \cr}
For example,
You water the garden, the garden get wet -> 1
You not watered the garden -> 2
The garden is not wet -> INVALID Inference as the garden can be wet if it rains.