The structure of butane-2, 3-diol is as
: $ C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\overset{\begin{smallmatrix} H \\ | \end{smallmatrix}}{\mathop{{{C}^{*}}}}}\,-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\overset{\begin{smallmatrix} H \\ | \end{smallmatrix}}{\mathop{{{C}^{*}}}}}\,-C{{H}_{3}} $
$ \because $ Optical isomers in compounds have similar asymmetric carbon atom, which are even in number $ ={{2}^{n}}-1 $ Here, $ n=2 $ $ \therefore $ total number of optically active stereoisomers $ ={{2}^{2}}-1=3 $