You don’t want to broadcast the call to permutedims here, you just need to call the function directly:
julia> x = reshape(1:12, (2, 3, 2))
2×3×2 reshape(::UnitRange{Int64}, 2, 3, 2) with eltype Int64:
[:, :, 1] =
1 3 5
2 4 6
[:, :, 2] =
7 9 11
8 10 12
julia> permutedims(x, (2, 1, 3))
3×2×2 Array{Int64, 3}:
[:, :, 1] =
1 2
3 4
5 6
[:, :, 2] =
7 8
9 10
11 12