Ok, now the clouds have parted! After some inspection, we see that the blue letter P doesn't have a "hole" where it needs to be. You can see that yourself by just dragging the white inner piece aside (and then Undo). (And you can also see why just deleting it didn't work.) We couldn't have guessed that from the JPG image you shared. Or that there's a separate object of the exact shape and size of the "hole". But now we can explain how to do this.
- Select both the main P object and the white inner object (you can do that, in this case, by Ctrl + a (select all) or by dragging a selection box around everything)
- Path menu > Difference
Note that the separate white piece disappears. It's more or less consumed in the process.
If you need to do this to a lot more text, there are some tricks to avoid having to do it one letter at a time. Let us know if you'd like to hear them. (I would explain, except that some people like to figure things out for themselves.)