Number of stereoisomers of 3-ethylpent-1-ene-1,4-diol
The answer lies in the double bond.  The alcohol on the double bond undergoes keto-enol tautomerism. The greatly more stable aldehyde effectively makes the vinylic alcohol non-existent. This removes a factor for stereoisomers.  six is an odd number of stereo isomers to have since 6 is factored to 2 and 3.  This implies a stereoisomer with 3 forms.  I think your teacher may be thinking of the trans, cis and aldehyde state of the alcohol to come up with six, but this would neglect a carbon stereo center. in this case 12 would be the correct answer. However you should ignore the tautomers and just assume aldehyde which means the answer should be 4.