stapeln
to stack
To place similar things neatly on top of one another so that a stack or pile is formed.
Er begann, die Bücher nach Größe zu sortieren und ordentlich zu stapeln.
He began sorting the books by size and stacking them neatly.

to stack
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to stack
To place similar things neatly on top of one another so that a stack or pile is formed.
Er begann, die Bücher nach Größe zu sortieren und ordentlich zu stapeln.
He began sorting the books by size and stacking them neatly.

The verb 'stapeln' (to stack) is directly related to the noun 'der Stapel' (the stack). A stack is the result of the action: when you stack books, a stack of books is created.
Kannst du mir helfen, den Stapel Papiere zu tragen?
Can you help me carry the stack of papers?
You can recognize the meaning of 'stapeln' (to stack) from the sentence structure. If it is used with an object, it is meant literally. If it is reflexive ('sich stapeln' (to pile up)), it means 'sich ansammeln' (to accumulate). If it appears with 'hoch' (high) or 'tief' (low), it is an idiom.
Ich muss noch die Wäsche stapeln.
I still have to stack the laundry.
In its literal meaning, 'stapeln' (to stack) is often used with flat, similar objects. Typical objects are books, plates, boxes, papers, or wood.
Wir müssen das Brennholz vor dem Winter ordentlich stapeln.
We need to stack the firewood neatly before winter.
The reflexive form 'sich stapeln' (to pile up) is often used for things that accumulate without active action. It usually has a negative connotation and refers to work, bills, or unfinished tasks.
Seit ich krank war, stapeln sich die E-Mails in meinem Posteingang.
Since I was sick, the emails have been piling up in my inbox.
The idiom 'tief stapeln' (to understate) is not to be understood literally. It means to be modest and deliberately present one's achievements or abilities as smaller than they are.
Obwohl er ein Experte ist, stapelt er immer tief und sagt, er wisse nicht viel.
Although he is an expert, he always understates things and says he doesn't know much.
The idiom 'hoch stapeln' (to exaggerate) is the opposite of 'tief stapeln' (to understate). It means to boast, exaggerate, or present abilities and possessions as greater than they really are.
Er hat bei seiner Bewerbung ganz schön hoch gestapelt und kann jetzt seine Versprechen nicht halten.
He really exaggerated in his application and now can't keep his promises.
to state / boast / report
'angeben' and 'hoch stapeln' can both describe someone presenting themselves as greater or better than is appropriate. 'angeben' is a normal colloquial verb for boasting, for example about money, knowledge, or success. 'hoch stapeln' is a fixed expression and more strongly emphasizes exaggerating or making promises that are too big. Learners may confuse the words because both can sound negative. 'angeben' fits boastful behavior in general; 'hoch stapeln' fits especially when someone presents their performance or abilities in an exaggerated way.

Beim Bewerbungsgespräch hat er ziemlich hoch gestapelt.
He exaggerated quite a bit in the job interview.
Er gibt ständig mit seinem neuen Auto an.
He is constantly boasting about his new car.