manch- (im Plural)
some
Means 'einige' (some) and refers to an indefinite number of people or things from a larger group.
Manche Leute mögen keinen Kaffee.
Some people don't like coffee.

some / many a
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some
Means 'einige' (some) and refers to an indefinite number of people or things from a larger group.
Manche Leute mögen keinen Kaffee.
Some people don't like coffee.

'Manch-' is declined like a definite article, for example 'dies-' (this). It agrees with the following noun in gender, number, and case.
Mancher Kollege hat sich darüber beschwert.
Some colleagues complained about it.
In the singular ('mancher', 'manche', 'manches'), the word often has a reflective or generalizing tone. It is used more often in written language and emphasizes that an experience applies to many individual cases.
Mancher Wunsch geht erst spät in Erfüllung.
Many a wish comes true only late.
Before an adjective, 'manch' can sometimes remain undeclined. This usage is rather literary or elevated.
Er erinnerte sich an manch guten Ratschlag seines Vaters.
He remembered many a good piece of advice from his father.
The expressions 'manch einer' (many a person) or 'so mancher' (quite a few / many a person) are fixed phrases. They refer to an indefinite, but not small, number of people.
Manch einer würde für diesen Job alles tun.
Many a person would do anything for this job.
some / several
'einige' and 'manch' can both mean an indefinite number from a larger group. 'einige' is very normal and neutral in everyday language. 'manche' in the plural often means something similar to 'einige', but sometimes sounds a bit more like a selection from the group. In the singular, for example 'mancher Mensch' (many a person) or 'mancher Tag' (many a day), 'manch' often sounds more general, reflective, or slightly elevated. Learners may confuse the words because neither gives an exact number. For simple everyday sentences, 'einige' is usually the safer choice.

Mancher Autofahrer fährt morgens zu schnell durch die Wohnstraße.
Many a driver drives too fast through the residential street in the morning.
Beim Training fehlten einige Spieler wegen einer Erkältung.
Some players were absent from training because of a cold.