I have attached an image that shows the reaction and each isomer formed.
The oxygen of the epoxide adds syn to the alkene, which means the oxygen is on one face of the molecule. Therefore, the epoxide has 2 chiral centers. The dimethyl amine is a nucleophile and it attack a carbon bound to oxygen in an sn2 fashion. This causes the epoxide ring to open, and after a proton transfer, the molecule now has a dimethyl amino group and an adjacent hydroxy group in an anti-relationship. The amine is able to attack either of the two carbons bound to the oxygen in the epoxide and this leads to two isomers. The isomers formed are a pair of enantiomers with the stereochemistry (R,R) and (S,S). Therefore, the second isomer that the question asks for is the (S,S) product shown.