I am planning a pergola using (6) 4x4 posts, spaced 10 feet apart, with 2x8
double beams.

The 2x6s will be spanning the 12 foot distance between the beams, with 2x2
slats on top of these every 2 feet.

Will the 2x6s be ok across the 12 foot span? is too much sag expected?

They will have 1 foot overhang on each end, so 2x6x14.

Thanks,

Paul