= Solution
Each atom supplies three displacement coordinates. Translational invariance gives three <acoustic phonon branches>[acoustic branches] for either structure, leaving
$$
\boxed{\begin{array}{c|cc}
&\text{acoustic}&\text{optical}\\
\text{tetragonal, }r=4&3&9\\
\text{orthorhombic, }r=8&3&21
\end{array}}
$$
These count branches at a general <wavevector>; a doubly degenerate pair still counts as two modes. The stated atom counts refer to primitive cells, so no additional centring factor is needed.
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