Positioning in a list

You can try

Pick[l,Exponent[x,l],0]   

{2 x, 4 x, 2 x, 4 x, 2 x}

or

Flatten[Take[l,#]&/@Position[Exponent[x,l],0]]     

Also if you want the positions try

Position[Exponent[x, l], 0]   

{{1}, {3}, {6}, {7}, {10}}

You might do like this:

l /. x -> 1 /. x_ /; x == 1 -> Nothing /. a_ -> a*x
(*   {2 x, 4 x, 2 x, 4 x, 2 x}   *)

Have fun!

l = {2 x, x, 4 x, x, x, 2 x, 4 x, x, x, 2 x};

s = Select[CoefficientList[l, x][[All, 2]], # > 1 &]*x

p = Position[l, Alternatives @@ Union[s]]

{{1}, {3}, {6}, {7}, {10}}

Extract[l, p]