I had the same issue with both the number 4 and number 8. I don't think I am weak but for the life of me, I couldn't get the 4 and the 8 coil to click pushing them in with my hand. I think what happens is when you push with your hand, because they are all the way back, you push them with an angle and it's impossible to get them in. What I end up doing is using a long pry bar and position one end on top of the coil with some padding so it doesn't damage the coil top and the other end elevated with some wooden block. Then I push down on the bar and the coil clicked right in I wouldn't believe it. You might want to give it a try. ymmv and I am not responsible if you damage the coil.
Here is an illustration of what I am talking about.