Let �s consider the grammar :
a) HOW, in the case of exclamations, must be followed by an adjective. It is the case in d) BUT ...
b) the sentence is ok grammaticaly.
c) in that case the noun after the adjective must have been plural as there is not the article A or AN.
d) the structure is incorrect grammaticaly.
Here are the general patterns I was taught for HOW and WHAT in exclamations :
HOW + adjective + subject + verb + !
For example : HOW INTERESTING YOUR QUESTION IS !
HOW INTERESTING HIS QUESTIONS WERE !
WHAT + A or AN + (adjective) + singular noun + (subject + verb) !
Examples : What A speech !
What A boring speech !
What A boring speech he did !
WHAT + - + (adjective) + plural noun + (subject + verb) !
Examples : What houses !
What strange houses !
What strange houses there are in this village !
But you can say too : What furniture in the houses ! .... because "furniture" is considered as a whole.
I think that the notion of LUCK in your example is considered as a precise event or circumstance at a precise moment, that explains the answer b) which can mean "a piece of luck" as we can say "a piece of furniture".
