die Faust
fist
The closed hand, with the fingers clenched tightly into the palm.
Aus Wut schlug er mit der Faust auf den Tisch.
Out of anger, he hit the table with his fist.

fist
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fist
The closed hand, with the fingers clenched tightly into the palm.
Aus Wut schlug er mit der Faust auf den Tisch.
Out of anger, he hit the table with his fist.

In its literal meaning, 'Faust' (fist) is often combined with certain verbs. Common expressions are 'die Faust ballen' (to clench one's fist), 'mit der Faust drohen' (to threaten with one's fist), or 'eine Faust machen' (to make a fist).
Vor dem Kampf ballte der Boxer die Fäuste.
Before the fight, the boxer clenched his fists.
The expression 'auf eigene Faust' (on one's own) is very common and means that someone does something independently and without help or instructions. The expression is grammatically fixed and is not changed.
Er beschloss, das Problem auf eigene Faust zu lösen.
He decided to solve the problem on his own.
The expression 'es faustdick hinter den Ohren haben' describes a person who is very clever or cunning. The 'es' is a fixed part of the expression.
Lass dich von ihrem Lächeln nicht täuschen, sie hat es faustdick hinter den Ohren.
Don't be fooled by her smile; she's craftier than she looks.
hand
'die Hand' and 'die Faust' are both connected to the arm and have to do with fingers. 'die Hand' means the normal body part used for grasping, writing, or feeling. 'die Faust' is a special form of the hand: the fingers are closed and tightly clenched. Learners may confuse the words because a fist is always a hand. But not every hand is a fist. If the hand is open or being used normally, you say 'Hand'. If it is closed, 'Faust' fits.

Vor dem Start ballte sie die Faust und atmete tief durch.
Before the start, she clenched her fist and took a deep breath.
Ben hält den Ball sicher in der Hand.
Ben holds the ball securely in his hand.