What is the "mechanism" of the decomposition of hydrogen peroxide?
Below is one way to write it that shows what the enzyme does and avoids the uncertainty of the details:

$$\ce{E + H2O2 -&gt; E-O + H2O}\tag{1}$$
$$\ce{E-O + H2O2 -&gt; E-O2 + H2O}\tag{2}$$
$$\ce{E-O2  -&gt; E + O2}\tag{3}$$

In words, the enzyme binds to the first molecule of hydrogen peroxide, release one molecule of water and holds on to the other oxygen atom (via the iron bound to heme bound to the enzyme). Then, the second molecule of hydrogen peroxide binds to the enzyme, which again release water and holds on to the second oxygen atom. Finally, the enzyme releases the two oxygen atoms in the form of the dioxygen molecule.

Alternatively, you could write the following three steps, giving even less information about what is happening in the enzyme:

$$\ce{E + 2H2O2 -&gt; [E\cdot H2O2\cdot H2O2]}\tag{A}$$
$$\ce{[E\cdot H2O2\cdot H2O2]-&gt; [E\cdot H2O\cdot H2O\cdot O2]}\tag{B}$$
$$\ce{[E\cdot H2O\cdot H2O\cdot O2] -&gt; E + 2H2O + 2O2}\tag{C}$$

In words, the enzyme first binds to the substrates, then catalyzes the reaction, and finally releases the products. While this in general might be a good way of describing the action of an enzyme, it is not quite correct for catalase, which releases one product before the second substrate binds. However, this might be the answer you are looking for at the IB level. I would ask the teacher for further clarification.