My Question :Is this lattice Distributive?
According to me it is bounded complemented lattice as every element has a complement.But they are not unique as d has c,f as complements and b has c,f as complements.So from here i am concluding it is not distributive lattice.
But i found somewhere it is saying that as it is not containing pentagon and diamond structure so it is Distributive .So there is Contradiction.
Please some clarify this.Thanks
It is indeed non-distributive - in particular, it does contain the pentagon structure ($N_5$, more commonly): just omit $b$ (or $c, d,$ or $f$). Since it contains $N_5$, it's not even modular.
Explicitly, here's one way modularity fails: $d\le b$ but $d\vee (c\wedge b)=d\not\ge b= (d\vee c)\wedge b$.
I am curious where you found the claim that it is distributive.
It is true that your lattice does not contain a copy of $N_5$ as an initial segment; but that's not relevant to distributivity concerns.