An enzyme is subject to allosteric regulation . how would you design an inhibitor of the enzyme that was competitive? non-competitive? irreversible?

Allosteric regulation or non-competitive is the same concept. Allosteric means, from the Greek, another place/other space.
So, starting by a non-competitive inhibitor, you could design an enzyme like a circle with two separate spots/recesses, symbolising connecting spots, one for the inhibitor and another one for the substrate. When the inhibitor is then placed into its position it changes the conformity of substrate's spot impeding it to connect.
For a competitive inhibitor, you could again design an enzyme like a circle but now only with a single binding spot where the inhibitor would connect so the substrate could not.
As for the irreversible inhibitor, you could design an enzyme as a circle again but it doesn't matter where you connect the inhibitor, whether on the substrate spot or not, as long as you make clear that there is a strong covalent bond between the enzyme and the inhibitor that doesn't allow the substrate to bind to the enzyme. You could represent this covalent bond by a simple trace connecting the enzyme to the inhibitor: -- .

The correct answer to this question would be c