Hello. As in your other post, I will try to give you an idea without giving the full solution.
This is a recursive function on a list. The two constructors for a list are [] and ::, meaning that every list is either [] or x :: xs with x an element and xs another list.
As a first idea, you can match the input list and see what you need to do in each case:
let rec remove_half1 l =
match l with
| [] -> (* what to do in the empty case? *)
| x :: xs -> (* what to do with x? what to do with xs? *)
The problem is that here you want to do a different thing with x according to the position in the list (even or odd). It means you need to know the position when you match on l, so your function must have an additional argument to remember the position.
let rec remove_half2 n l =
match l with
| [] -> (* ... *)
| x :: xs -> if (* test on n *) then (* ... *) else (* ... *)
If you manage to write this remove_half2 it will have the following type:
remove_half2 : int -> `a list -> `a list
but remove_half does not have this int parameter. It means that you need to run remove_half2 with an initial value so that you have the right type for your final function.
let remove_half l = remove_half2 (* initial value *) l
Good luck!