
beachten
to note
To take note of something and take it into account; to direct one's attention to something.
Bitte beachten Sie die geänderten Öffnungszeiten.
Please note the changed opening hours.
to note / observe
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to note
To take note of something and take it into account; to direct one's attention to something.
Bitte beachten Sie die geänderten Öffnungszeiten.
Please note the changed opening hours.

to observe
To follow and comply with rules, laws, or regulations.
Wer die Verkehrsregeln nicht beachtet, riskiert ein Bußgeld.
Anyone who does not observe the traffic rules risks a fine.

to notice
To show appreciation or respect to someone or something; to notice someone.
Obwohl er ein Experte ist, werden seine Ratschläge kaum beachtet.
Although he is an expert, his advice is hardly noticed.
'Beachten' (to note / observe) is an inseparable verb with the prefix 'be-'. It is always transitive, meaning it needs a direct object in the accusative.
Der Fahrer hat das Stoppschild nicht beachtet.
The driver did not observe the stop sign.
This verb is often used in formal contexts such as instructions, official notices, or on signs. The request 'Bitte beachten Sie, dass ...' (Please note that ...) is very common.
Bitte beachten Sie, dass das Museum montags geschlossen ist.
Please note that the museum is closed on Mondays.
When it comes to complying with rules, 'beachten' (to observe) is often combined with these nouns: die Regeln beachten (to observe the rules), die Vorschriften beachten (to observe the regulations), das Gesetz beachten (to observe the law), die Anweisungen beachten (to follow the instructions).
Im Straßenverkehr muss man viele Regeln beachten.
In road traffic, you have to observe many rules.
In the meaning 'to notice someone', the verb is often used in the passive and with a negation to express that someone is being ignored.
Seine Ideen wurden von den Kollegen kaum beachtet.
His ideas were hardly noticed by his colleagues.
to pay attention / to respect
Achten auf and beachten both direct attention to something. “Achten auf” mainly means being attentive or careful, while “beachten” more strongly expresses consciously taking a requirement into account or following it. “Achten auf” usually fits a warning, while “beachten” fits a rule or instruction.

Bitte beachten Sie die Sicherheitshinweise am Eingang.
Please observe the safety instructions at the entrance.
Bitte achten Sie auf die Stufe am Eingang.
Please watch out for the step at the entrance.