This is just off the top of my head, and could probably be shorter. This assumes that @array is a multiple of 4 elements, and drops anything that's modulo 4:

my @array = (1 .. 8);
my @other = ();

while ((@array % 4) == 0)
{
    push(@other, $array[$#array], @array[0, 1], $array[$#array - 1]);
    splice(@array, 0, 2); splice(@array, -2);
}
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If you want to handle a remainder chunk specially, you can do so after the while exits...

Edit: This is bad in that the modulo/lost elements are from the center of the list, not the end. Unless you are certain that you list is always a multiple of 4 in length, you'll definitely want to handle the remainder.