I don't know why my solutions manual says these are enantiomers:
The Fisher projections I drew suggest that these are identical compounds.
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The solutions manual is correct, they are enantiomers. The compound on the left is (R)-2-chloro-(S)-3-butanol and the compound on the right is (S)-2-chloro-(R)-3-butanol. Try to use the "R\S" nomenclature system on the 2 chiral carbons, that should help figuring out whether they are identical [(R,R and R,R), (S,S and S,S), (R,S and R,S), (S,R and S,R)] enantiomers [(R,R and S,S), (R,S and S,R), (S,R and R,S)] or diastereomers [(R,R and R,S), (R,R and S,R), (S,S and S,R), (S,S and R,S)].
In the following figure, everything on the left is identical and everything on the right is identical.
See this page for how to draw Fischer Projections.