Rechts vs. Rechte
In German, both rechts and Rechte relate to the direction right. However, they are different parts of speech and are not interchangeable. The core difference is that rechts is an adverb of direction, while Rechte is a noun.
Rechts
A1This is an adverb that indicates a direction or a location. It answers the questions Where? (Wo?) or Where to? (Wohin?) and means on the right or to the right. As an adverb, its form never changes and it is written in lowercase unless it's at the beginning of a sentence.
Das Badezimmer befindet sich am Ende des Flurs rechts.
(The bathroom is located at the end of the hall on the right.)
Bitte biegen Sie an der nächsten Ampel rechts ab.
(Please turn right at the next traffic light.)
Mein Haus ist das dritte von rechts.
(My house is the third from the right.)
Im Theater saß ich rechts von der Bühne.
(In the theater, I sat to the right of the stage.)
Rechte
B1This is a feminine noun (die Rechte) that refers to the right hand or the right side as a concrete thing. As a noun, it is always capitalized. It is often used with an article (like die, seine, meine) or a preposition that requires a noun.
Der Tennisspieler hat eine sehr kraftvolle Rechte.
(The tennis player has a very powerful right hand.)
Er verletzte sich an der Rechten und kann nicht schreiben.
(He injured his right hand and cannot write.)
Sie hob ihre Rechte, um zu schwören.
(She raised her right hand to swear an oath.)
Auf der Rechten sehen Sie den alten Marktplatz.
(On the right side, you see the old market square.)
Summary
In short, use the lowercase adverb rechts to describe a direction or location, as in turn right (biegen Sie rechts ab). Use the capitalized noun Rechte when you are referring to the right hand or the right side as a specific object or entity, as in his right hand (seine Rechte).