Let this be the rows of chairs:

[] [] []

[] [] []

Let their be siblings \(x\) and \(x\), \(y\) and \(y\), and \(z\) and \(z\). Beginning with placing the \(x\) siblings, there are 6 options for the first sibling obviously, and 4 options for the second sibling, giving us 24 ways of placing them (6*4):

[x1] [] []

[x2 not allowed] [] []

Let's say we go with this arrangement:

[x1] [] []

[] [x2] []

We must place one of the y siblings in the rightmost column, or else the z siblings will be front and behind each other (there are two ways to do this):

[x1] [] []

[] [x2] [y]

Then there are two ways of placing the other y sibling (row 1 column 2 or row 2 column 1), giving us 4 ways of placing the y siblings (2*2), but then we could also swap it so that sibling y2 could be in the right most column and y1 is in the other spots, givings us 8 ways of placing the y siblings:

[x] [] []

[y2] [x] [y1]

And then the z siblings go in automatically, with 2 ways, as we can swap z1 and z2. this gives us \(24*8*2=\boxed{384}\) ways. Sorry if my explanations a bit long, this problem I found hard to explain without going super in depth.