Let's look at an example
The motion is: This house would take down public statues of people guilty of racist attitudes or behaviour.
The proposition say that the existence of these statues in public places endorses racism and is an assault on people of colour, so they must all be taken down, but legally, by the authorities responsible for those public places, not by direct action. That's their mechanism. Implicit in the mechanism is that removing statues is the best way to counter racism.
The opposition could simply accept this mechanism, and argue against the dismantling of statues on the grounds of free speech and opposition to censorship, setting freedom of speech up as a higher good than opposition to racism. This would create a clear divide between them and the proposition. However, it would also concede quite a lot of ground to the proposition. It would give them a monopoly of the case for anti-racism. Better, in fact, for the opposition to advance into the proposition's ground and to take over some of their anti-racism.
They can do this by agreeing with the proposition that the existence in the middle of cities with a significant black population of statues of slave owners, implicitly celebrating their 'achievements', is an assault on people of colour. Then, they can say that there is a better way of dealing with this assault. They would add plaques to the statues detailing the racist actions and attitudes of these once celebrated people. This is their counter-mechanism: a course of action which is different from the one proposed in the motion (the statues stay up), while accepting the existence of the problem implicit in the motion (the public celebration of racists is wrong).
This action would have the advantage of both supporting one of the opposition's strongest arguments (censoring history by editing out the parts of it we do not like will stop people from understanding it), while also supporting one of the proposition's strongest arguments (racism must not be celebrated). It is also, like all the best mechanisms, practical (plaques could be added easily and at very little expense), enforceable (provided the plaques were accurate, few could object to them) and simple (it is very easy to explain and justify in the limited time allowed in a debate). It is also easier to defend than the proposition's mechanism, as it doesn't raise the tricky question of what should replace the statues once they are taken down.