
peinlich
embarrassing
Causing a feeling of embarrassment, shame, or discomfort.
Es war mir furchtbar peinlich, als mein Handy im Theater klingelte.
I was terribly embarrassed when my phone rang in the theater.
embarrassing / meticulous
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embarrassing
Causing a feeling of embarrassment, shame, or discomfort.
Es war mir furchtbar peinlich, als mein Handy im Theater klingelte.
I was terribly embarrassed when my phone rang in the theater.

meticulous
Extremely precise, overly careful and conscientious. Often in the phrase 'peinlich genau'.
Er achtet immer peinlich genau darauf, dass sein Schreibtisch perfekt aufgeräumt ist.
He always makes meticulously sure that his desk is perfectly tidy.

penal / torturous
An outdated legal meaning for something connected with corporal punishment or torture.
Die „peinliche Befragung“ war im Mittelalter eine Methode, um Geständnisse zu erzwingen.
The 'peinliche Befragung' (interrogation under torture) was a method used in the Middle Ages to force confessions.
The word 'peinlich' (embarrassing / meticulous) is derived from 'die Pein' (torment, pain). This explains the old meaning related to torture and also the modern meaning: an embarrassing situation causes a kind of emotional pain.
Sein unhöfliches Verhalten war eine Pein für die ganze Familie.
His rude behavior was a torment for the whole family.
To express for whom a situation is embarrassing, you use the structure 'Es ist + [dative pronoun] + peinlich' (It is embarrassing for [someone]). The subject of the sentence is often 'es' (it).
Es war ihm sehr peinlich, dass er den Namen vergessen hatte.
He was very embarrassed that he had forgotten the name.
In the meaning 'übertrieben sorgfältig' (overly careful), 'peinlich' is almost always used as an intensifier before another adjective such as 'genau' (precise) or 'sauber' (clean). The most common combination is 'peinlich genau' (meticulously precise).
Sie achtet peinlich genau auf die Einhaltung der Regeln.
She pays meticulous attention to compliance with the rules.
When 'peinlich' stands alone, it almost always means 'unangenehm' (embarrassing / unpleasant). When it stands directly before an adjective such as 'genau' (precise) or 'sauber' (clean), it means 'extrem' (extremely) or 'übertrieben' (excessively).
Die Stille im Raum war peinlich.
The silence in the room was embarrassing.
The meaning 'connected with corporal punishment' is outdated. Today you will find it only in historical texts, often in connection with the legal system of the Middle Ages.
Die „peinliche Gerichtsordnung“ regelte schwere Strafverfahren.
The 'peinliche Gerichtsordnung' (penal court ordinance) regulated serious criminal proceedings.
to move / lay / misplace
Peinlich describes a situation that causes embarrassment or shame. In the meanings given here, verlegen is a verb, however, and means to move something. So use peinlich for your own embarrassed reaction and verlegen for a rescheduled appointment.

Nach meinem Versprecher vor allen Gästen war mir die Situation peinlich.
After I misspoke in front of all the guests, I found the situation embarrassing.
Wegen meines Versprechers mussten wir den Termin auf morgen verlegen.
Because I misspoke, we had to reschedule the appointment for tomorrow.