When playing Kings Quest 4 we need to put in a word from the manual. When I alt+tab out and come back its no longer full screen, how do I fix this?

By looking in the right document.
You will want to look at page one of the "Reference Card".
Somewhat surprised no-one bothered to remove this nuisance before release..

Easy enough to do, but because of the potential legality of it, I am reluctant to post it. If the GOG team wants to eliminate it, they can contact me.

Legality? What an odd notion.
The whole GOG:com catalogue is filled to the brim of titles that (one way or the other) have been ripped of their original DRM. As NOT having any DRM is very much part of the whole deal here, I would think it safe to assume that legality is not an issue at all.

Not referring to GOG, but for me. It could be considered a "crack". Don't get me wrong, I would just as soon have it gone from the release, myself.

Lots of titles here use the same "cracks" (anyone who knows how to do a binary filecompare can test for themselves) that have been floating around the net for ages, so I really don't get your point.
It is interesting however, that the version of KQIV from here seems to be a somewhat newer version than the 11 (illegal) copies that I managed to find by googling for a few minutes. Are you sure that whatever "crack" you happen to have in your possession, but unwilling to share due to "legality" issues, is indeed for the same (1.006.004) version?

Have you tried emailing GOG? I'd certainly like to get rid of the copy protection.

I actually have my manual from my Amiga500 version still.

no you have to correct manual that GOG gives you but the password is cryptic at first.

go to page 5 of the manual and you will see the table thenumbers on the far left indicate the page number the numbers in the middle represent paragraph number and the numbers on the right represent the number of the work like the 1st word of the paragraph 4th word of the paragraph and so on.

once you do it a few times its ewasy to get the hang out the annoying thing is you must enter it evertime you restart

The table of codes is actually faster way to get past the copy protection than reading through the original manual's pages.

The table of answers is actually missing quite a few entries, some are even completely wrong after looking at the script that handles it. It's been that way since at least the 1997 King's Quest Collection, which is based off the Roberta Williams Anthology.