einhalten
to keep / comply with
To follow or fulfill something that has been specified or promised, such as a rule, deadline, or agreement.
Es ist wichtig, die vereinbarten Fristen einzuhalten.
It is important to keep the agreed deadlines.

to keep / to comply with
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to keep / comply with
To follow or fulfill something that has been specified or promised, such as a rule, deadline, or agreement.
Es ist wichtig, die vereinbarten Fristen einzuhalten.
It is important to keep the agreed deadlines.

'Einhalten' (to keep / to comply with) is a separable verb. The prefix 'ein-' stands at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Der Fahrer hielt die Geschwindigkeitsbegrenzung genau ein.
The driver kept exactly to the speed limit.
The verb consists of 'ein' and 'halten'. You can imagine it as staying ('hält') within ('ein') a certain framework, such as a rule or a deadline, and not leaving it.
Bitte halten Sie die Sicherheitsvorschriften ein.
Please comply with the safety regulations.
The thing that is complied with or kept (a rule, an appointment, a promise) is always in the accusative. You ask: Whom or what am I keeping/complying with?
Wir müssen den Zeitplan einhalten.
We have to keep to the schedule.
'Einhalten' (to keep / to comply with) is very often used with abstract nouns that express an obligation: 'eine Frist einhalten' (to meet a deadline), 'Regeln einhalten' (to follow rules), 'ein Versprechen einhalten' (to keep a promise), 'eine Vereinbarung einhalten' (to honor an agreement).
Alle Mitarbeiter müssen die neuen Datenschutzrichtlinien einhalten.
All employees must comply with the new data protection guidelines.
The meaning 'innehalten' (to pause) or 'eine Pause machen' (to take a break) is rare and is used almost only in literature or in very elevated language. It is unusual in everyday speech.
Der Wanderer hielt einen Moment ein, um die Aussicht zu genießen.
The hiker paused for a moment to enjoy the view.
to hold
'sich halten an' and 'einhalten' both have to do with rules, appointments, or agreements. 'sich an etwas halten' is often used when a person acts according to a rule: you stick to the house rules or to a plan. 'einhalten' emphasizes more strongly that a requirement is actually fulfilled, for example a deadline, an appointment, or a promise. The words can be confused because they fit in similar situations. Often, 'eine Frist einhalten' (to meet a deadline) sounds more natural than 'sich an eine Frist halten', while 'sich an die Regeln halten' (to stick to the rules) is very common.

Ich halte den Termin morgen ein, obwohl ich am Wochenende wenig Zeit hatte.
I will keep the appointment tomorrow, even though I had little time over the weekend.
Im Zug halten sich die meisten Fahrgäste an die Ruhezeiten.
On the train, most passengers stick to the quiet hours.