The red plastic is a device to assist clearing lint build up and is not critical for the operation of the shuttle (esp if you perform normal housekeeping and clean this area regularly, as you should)
Check there is no damage to the surface of the red plastic, as this will cause problems if not smooth (jamming)
It fits between the fixed half moon metal shuttle and the outer body.
There is a small notch which locates it into position.
Tilt the machine back 30 - 45 degrees to make the insertion easier, then fit the hook then the collar....flick the retaining clips to secure.
I always find this easiest with the machine tilted back......reduces the chances of bits falling out while you put the next piece in.
This is for front loading bobbin..........
The Shuttle hook will look very much like this, and marries this to the "half moon" of the fixed shuttle.
The retaining collar ring that holds it all together has a plate like protrusion (like bull horns), this faces to the top and to the back.......there should be a small lug (or two) with corresponding small hole or slot on the fixed housing (hook race) that locates the ring tightly in the correct position.
There should be 2 swivel arms (black plastic at 4 o'clock & 8 o'clock)) that move to hold the whole thing together by clipping onto a small lug on each side of the ring.
If you tip the machine on its back while you do all this, it makes the process easier, as things are less likely to fall out.........support the back with a soft object for convenience (tissue box, pillow etc)
The bobbin case goes in after the housing is assembled, if you try to do it first, it will prove more difficult.
If this is not quite accurate for your model a photo of the bits would be helpful
The finished assembly looks like this: