The given reaction is an example of:
${\mathrm{Fe}}_2{\mathrm{O}}_3+2\mathrm{Al}\to {\mathrm{Al}}_2{\mathrm{O}}_3+2\mathrm{Fe}$

We are aware that a redox process involves simultaneous oxidation and reduction. Because electrons are lost during the oxidation process, the element's oxidation number rises. The element is reduced or a reduction process occurs if the oxidation number decreases in the same way.

A synthesis reaction is another name for a combination reaction. 

A substitution reaction is another name for a displacement reaction. A metathesis reaction is another name for a double displacement reaction.

Here, oxygen is displaced from iron to aluminium. Therefore, it is a displacement reaction.

Thus, the given reaction is an example of a displacement reaction.

Hence, the correct option is (D)