Identify the reactant and reagent

The given reaction is: $(CH_3)_3C-Br \xrightarrow{H_2O} (CH_3)_3C-OH$

Here, tert-butyl bromide reacts with water to form tert-butyl alcohol.

What change is happening?

The bromine atom $(-Br)$ attached to the carbon is replaced by the hydroxyl group $(-OH)$.

So, the transformation is: $R-Br \rightarrow R-OH$

Classify the reaction

Since one group ($Br$) is replaced by another group ($OH$), this is a substitution reaction.

More specifically, tert-butyl bromide in water undergoes nucleophilic substitution (generally via $S_N1$ mechanism because tert-butyl carbocation is stable).

Check the options

• A: elimination reaction — Incorrect, because no alkene is formed.
• B: substitution reaction — Correct, because $Br$ is substituted by $OH$.
• C: free radical reaction — Incorrect, no radical conditions are given.
• D: displacement reaction — Although substitution can also be described as displacement in a broad sense, in standard organic classification for this reaction, the correct term is substitution reaction.

Final answer

$\boxed{\text{B: substitution reaction}}$