zurückgehen
to go back
To return to a place one came from.
Nach dem Spaziergang gehen wir wieder nach Hause zurück.
After the walk, we'll go back home.

to go back / decline
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to go back
To return to a place one came from.
Nach dem Spaziergang gehen wir wieder nach Hause zurück.
After the walk, we'll go back home.

'Zurückgehen' (to go back/decline) is a separable verb. The prefix 'zurück-' stands at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Wann gehst du heute Abend nach Hause zurück?
When are you going back home tonight?
Since 'zurückgehen' (to go back/decline) describes movement, the perfect tense is always formed with the auxiliary verb 'sein' (to be), not with 'haben' (to have).
Die Touristengruppe ist bereits zum Bus zurückgegangen.
The tourist group has already gone back to the bus.
In the meaning 'to have its origin', 'zurückgehen' (to go back to) is always used with the preposition 'auf' and the accusative. This structure is fixed.
Der Name der Stadt geht auf einen römischen Kaiser zurück.
The name of the city goes back to a Roman emperor.
When 'zurückgehen' (to decline) means 'to decrease' or 'to become less', the subject is often an abstract quantity. Typical examples are numbers, prices, interest, or temperature.
Die Arbeitslosigkeit ist in diesem Jahr leicht zurückgegangen.
Unemployment has declined slightly this year.
to fall
'fallen' and 'zurückgehen' can both mean that something decreases. 'fallen' is often used with numbers, prices, temperatures, or a level. It sometimes suggests a clear downward movement. 'zurückgehen' tends to emphasize that an amount, a number, or an intensity is decreasing, for example visitor numbers, pain, or noise. The words can be confused because both fit similarly in many situations. As a simple guide: prices and temperatures very naturally 'fallen'; numbers, demand, or complaints very naturally 'gehen zurück'.

Nach den Ferien gehen die Besucherzahlen im Schwimmbad zurück.
After the holidays, visitor numbers at the swimming pool decline.
Wegen des Angebots fallen die Preise in diesem Geschäft.
Because of the special offer, prices are falling in this store.