This Type, These Type, This Types, These Types

Both 'type' and 'types' can be correct, as long as everything agrees in number.

In a sentence that has a phrase like "this/these type/types of [noun]" you need everything to agree in number. That is, you need everything to be singular or everything to be plural.

'This' and 'type' are singular, so use them together with a singular noun.

'These' and 'types' are plural, so use them together with a plural noun.

Both of the following sentences are correct:

• I detest these types of programmes. [everything is plural]
• I detest this type of programme. [everything is singular]

'Kind' is another word that does this:

• I love this kind of book. [everything is singular]
• I love these kinds of books. [everything is plural]

I hope this helps.