Confused about the order of determiners

Question

the last two books

the two last books

Like the phrase" the two best friends"(I think) the latter would be correct. ......

my last two books

my two last books

I am confused which of those could be correct!

Answer 1

Short answer:

USE THIS: the last two books
BUT NOT: the two last books

USE THIS: my last two books
BUT NOT: my two last books

Your examples are not similar to the two best friends because best is an adjective, not a determiner (or not a postdeterminer, to be specific).

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Grammar points:

The two links given by CopperKettle (one on The Internet Grammar of English and the other from English Grammar Today) are almost "just enough", but because neither mentions clearly what would be the order of ordinal and cardinal numbers when they co-occur, I decide to post this answer.

Let's review the basics. I'll base my explanation on English Grammar Today, but either source (or any of most grammar books) should be fine.

Where do determiners go? -- Determiners come first in noun phrases, before adjectives and noun modifiers. The basic order is:

determiner(s) 　 adjective(s) 　 noun modifier(s) 　 head noun

For example, in three big, old kitchen tables, "three" is a determiner, "big, old" are adjectives, and "kitchen tables" is the head noun. (You can divide kitchen tables further, but it's not really relevant to our discussion, which is about ordinal and cardinal numbers.)

^{​　　　　SIDE NOTE: And this is why we write the two best friends, not the best two friends.
​　　　　The is an article, which is a determiner; two is a number, which is another determiner; but best is an adjective.
​　　　　So, best must be right next to friends, which is the head noun of the two best friends.}

More than one determiner -- When there is more than one determiner in a noun phrase, we put them in a fixed order:

quantifier 　 article 　 demonstrative 　 possessive 　 number

Here are some of these determiners:

• quantifier e.g. all, both, some
• articles: a/an, the
• demonstrative: this, that, these, those
• possessive: e.g. my, her, our, Anna’s
• number: one, three, 26

So, it's now clear that the, which is an article, and my, which is a possessive pronoun, must come before last and two. But which comes first: last or two?

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Ordinal and Cardinal Numbers

To decide which comes first between last and two, you need to know that last is an "ordinal number" and two is a "cardinal number".

An ordinal number is about the position of something in a series, e.g., first, second, third, ..., last are ordinal numbers.

A cardinal number is about counting: one, two, three, ..., 41, 42, and so on.

When we use both ordinal and cardinal numbers, the ordinal number comes first.

"When a cardinal number and an ordinal number modify the same noun, the ordinal number always precedes the cardinal number:

• The first two operations were the most difficult to watch.

• The second three innings were quite dull.

In the first example, the ordinal number first precedes the cardinal number two. Both first and two are determiners. In the second example, the ordinal number second precedes the cardinal number three. Both second and three are determiners. Try reading the sentences with the ordinal and cardinal numbers reversed. They simply sound wrong."
(Michael Strumpf and Auriel Douglas, The Grammar Bible. Owl Books, 2004)
_{(via: About Education)}

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So, to answer your question once again, these are correct: the last two books, my last two books.