What is an example of chemical reaction that can be assisted by both an inorganic catalyst and an enzyme?
A good example is the conversion of hydrogen peroxide to oxygen and water
$$\ce{2H2O2 -&gt;2H2O + O2}$$
It can be catalyzed by catalase, which has one of the highest known turnover numbers, or by an inorganic catalyst such as manganese(IV) oxide or lead(IV) oxide.
This has been suggested for instance as an educational project by the University of York (see references).
References

Decomposing hydrogen peroxide. Chemistry Review (1995), Volume 5, Number 1, p. 30. https://www.york.ac.uk/chemistry/schools/chemrev/