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what is "determiners"and "predeterminers"? Show some examples

Determiners:

Determiners are words like the, an, my, some. They are grammatically similar. They all come at the beginning of noun phrases, and usually we cannot use more than one determiner in the same noun phrase.

Articles:

• a, an, the

Possessive Adjectives:

• my, your, his, her, its, our, their, whose

Other determiners:

• each, every
• either, neither
• some, any, no
• much, many; more, most
• little, less, least
• few, fewer, fewest
• what, whatever; which, whichever
• both, half, all
• several
• enough

Predeterminers: 

The predeterminers occur prior to other determiners (as you would probably guess from their name). This class of words includes multipliers (double, twice, four/five times . . . .); fractional expressions (one-third, three-quarters, etc.); the words both, half, and all; and intensifiers such as quite, rather, and such.

The multipliers precede plural count and mass nouns and occur with singular count nouns denoting number or amount:

• This van holds three times the passengers as that sports car. 
• My wife is making double my / twice my salary. 
• This time we added five times the amount of water.

In fractional expressions, we have a similar construction, but here it can be replaced with "of" construction.

• Charlie finished in one-fourth [of] the time his brother took. 
• Two-fifths of the respondents reported that half the medication was sufficient.

The intensifiers occur in this construction primarily in casual speech and writing and are more common in British English than they are in American English. The intensifier "what" is often found in stylistic fragments: "We visited my brother in his dorm room. What a mess!"

• This room is rather a mess, isn't it? 
• The ticket-holders made quite a fuss when they couldn't get in. 
• What an idiot he turned out to be. 
• Our vacation was such a grand experience.

Half, both, and all can occur with singular and plural count nouns; half and all can occur with mass nouns. There are also "of constructions" with these words ("all [of] the grain," "half [of] his salary"); the "of construction" is required with personal pronouns ("both of them," "all of it").