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There are two complement pair here ->

Meet(4,3) -> 1

Join(4,3) ->12

There is another pair here -> Upper & Lower bounds are also compliments of each other.

Meet(1,12)->1

Join(1,12) ->12
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Complement pair of a lattice will have both LUB (Least Upper Bound), and GLB (Greatest Lower Bound). LUB and GLB of a lattice are unique, and in this case, they are $12$ and $1$ respectively.

A complement pair of lattices will have $12, 1$ as LUB and GLB respectively.

But here we see pair $(4,6)$ which has LUB $12$ and GLB $2$.

$(2,3)$ have LUB $6$ and GLB $1$.
$(3,4)$ has LUB $1$ and GLB $12$.

Other pairs need not be compared since they are directly joined with a line.

Therefore, I think that the given lattice has $1$ complement pair.
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