"Tell this to your sister."
Translation:यह अपनी बहन को बताओ।
Hindi has a reflexive pronoun (अपना/अपनी/अपने ) that you use when you want to refer back to the subject of the sentence. Imperative sentences (used to give commands and make requests) such as 'Tell this to your sister' have 'you' as the implicit subject. So, while saying 'your' which is pointing to the subject of the sentence, you have to use अपनी, instead of the actual Hindi word for 'your' (तेरी/तुम्हरी/आपकी).
The level of formality will be determined by the verb conjugation.
यह अपनी बहन को बता - is in the तू - level of formality
यह अपनी बहन को बताओ - is in the तुम -level of formality
यह अपनी बहन को बताइए - is in the आप -level of formality
What LangPhile means is that in colloquial speech, the verb forms which are associated with तुम are used with आप as a sort of intermediate level of formality (especially with older family members).
So, it wouldn't be unheard of to say 'यह अपनी बहन को बताओ' to someone you address with आप.
When you want a pronoun to refer back to the subject of the sentence, you use अपना/अपनी/अपने.
For example, in 'I am eating my apple', the pronoun 'me' is referring to the subject of the sentence 'I'. Therefore, you would say, मैं अपना सेब खा रहा हूँ। with अपना instead of मेरा.
The sentence 'Tell this to your sister' has 'you' as the implicit subject because it is a command and he pronoun 'your' refers back to it. As a result, अपनी has been used.