Identify the type of the following reaction?

The given reaction involves the treatment of a sodium alkoxide (sodium 3-ethylpentan-3-olate) with an alkyl halide (methyl bromide) to form an ether (3-ethyl-3-methoxypentane).

This is a classic example of the Williamson ether synthesis.

The general reaction is given by:
$R-O^{-}Na^{+} + R'-X \rightarrow R-O-R' + NaX$

The reaction proceeds via an $S_N2$ mechanism where the alkoxide ion acts as a nucleophile and attacks the unhindered methyl carbon, displacing the bromide ion.

Answer: Williamson synthesis