No preposition needed here. I arrive home at 6:00. I arrive home and am greeted by my dog.

Is this preposition necessary？ 1 She reached New York . She arrived in New York. 2 she reached there she arrived there she got there why in the second set of sentences, there is no preposition such as IN or at ? thanks for your help

Just check out a good dictionary. Example: https://www.macmillandictionary.com/dictionary/american/arrive

Si, ya hablo un español pero conviene aprender más. Ya que siempre me esta corrigiendo mi familia cuando hablo. Soy de los estados unidos y mi lenguaje nativa es inglés

There is no difference essentially .In this context you always use It without the preposition, like in "go home". I will give some exemples when you can use "at": I'm checking my saving accounting at home. I'm working at home now.