Question

When hydrochloric acid reacts with sodium hydroxide to produce sodium chloride and water, is that a double displacement reaction?

Answer 1

Yes it is, it can be helpful to think of water as hydrogen hydroxide to see why this is true.

HCl + NaOH -> NaCl + HOH

Double diplacement reactions are summarized as follows:
AB + CD -> AD + CB

H = A
Cl = B
Na = C
OH = D

Water is HOH or AD

Here is a video to help out with other acid-base reactions.