You sort of twist it in the hole ....sort of butterfly valve style .by knocking it with a blunt chisel on one side ..
then you are sometimes able to manipulate it from there.
Sometimes you have to push it right in and sort of distort it with wallops from the chisel ...to get it out ........mind the edges of the hole ...dont damage because ..they have to Seal again !!!
The new one needs to be knocked in squarely with hilomar as sealant.
what's the betting that other core plugs leaking will follow shortly
i have one under the bell housing to change on the same engine as yours .