Number of stereoisomers of tetramethylspirononane
The compound 2,3,7,8-tetramethylspiro[4.4]nonane has five potential stereogenic or pseudoasymmetric centres: the four C atoms with the methyl substituents and the spiro atom. In total there are $2^5=32$ possible configurations. However, many of these combinations are actually identical compounds.

A simple and obviously exhaustive (but also exhausting) approach is to draw all 32 configurations and name them. (This approach may also be used to check the results if someone finds a more elegant solution.) The resulting names for the 32 combinations are:


(2​R,3​R,7​R,8​​R)-2,3,7,8-tetramethylspiro[4.4]nonane (2 times)

(2​R,3​R,7​R,8​S)-2,3,7,8-tetramethylspiro[4.4]nonane (8 times)

(2​R,3​R,7​S,8​S)-2,3,7,8-tetramethylspiro[4.4]nonane (4 times)

(2​R,3​S,5​r,7​R,8​S)-2,3,7,8-tetramethylspiro[4.4]nonane (4 times)

(2​R,3​S,5​s,7​R,8​S)-2,3,7,8-tetramethylspiro[4.4]nonane (4 times)

(2​R,3​S,7​S,8​S)-2,3,7,8-tetramethylspiro[4.4]nonane (8 times)

(2​S,3​S,7​S,8​S)-2,3,7,8-tetramethylspiro[4.4]nonane (2 times)



Therefore, there are seven different combinations.