Teachers, this question is simple:

this kind of thing O

this kind of things X

these kinds of thing X

these kinds of things O

Did I check them correctly?
yes you did (assuming O means correct)
Nona The Brityes you did (assuming O means correct)
then, "many kinds of English" should be "many kinds of Englishes"?
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I think Nona may have taken a break.

"thing" is countable; "English" is not.
So the two are not comparable.
We can't take a pattern for countable nouns and apply it to non-countable nouns and expect to get correct results!

many kinds of things
many kinds of streets
many kinds of tables
many kinds of films

many kinds of meat
many kinds of sugar
many kinds of forgiveness
many kinds of English

How about "many kinds of proteins"
AnonymousHow about "many kinds of proteins"
That's fine. You'll find that expression all over the place in cell biology texts, for example.

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nona the brit yes you did (assuming O means correct)
No, all four are correct.

1) "kind of thing" is a singular noun phrase.
2) "kind of things is another singular noun phrase"
3) "kinds of thing" is the plural of the phrase at 1) above
4) "kinds of things" is the plural of the phrase at 2) above.

2) is used about twice as often as 1) on the web, so any descriptivist will tell that is 1 is correct then 2 certainly is.