If $M$ is *smooth* and $\dim M =3$, then the answer is *always*. This is a theorem due to Shokurov, see

V.V. Shokurov: [*Smoothness of a general anticanonical divisor on a Fano variety*][1],  Math.
USSR, Izv **14**, 395-405 (1980).


  [1]: http://www.google.it/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0CCMQFjAA&url=http%3A%2F%2Fwww.maths.ed.ac.uk%2Fcheltsov%2Fshokurov%2Fpdf%2Felephant.pdf&ei=f0LKVOPtF9fvaO65gYgC&usg=AFQjCNFPX_liED_da0wBLoycMKGuf04Amg&bvm=bv.84607526,d.d2s