Learn Arabic (Modern Standard): رحبت بنا ترحيبا حارا.

This is a classic Arabic structure called the cognate accusative. Instead of using a standalone adverb for 'warmly', Arabic often repeats the verb's verbal noun (masdar) and attaches an adjective to it. Literally, this translates to 'She welcomed us a warm welcoming'.

Why do we use the preposition بـ in بنا instead of just attaching a direct object pronoun like رحبتنا?

The verb رحب (to welcome) requires the preposition بـ to indicate the person being welcomed. Therefore, 'she welcomed us' must be expressed as رحبت بنا, rather than taking a direct object pronoun suffix.

Why do both ترحيبا and حارا take the accusative '-an' ending?

ترحيبا is in the accusative case (mansub) because it acts as the absolute object of the verb. حارا is an adjective describing that noun, so it must perfectly match its case, gender, and definiteness, resulting in both words taking the indefinite accusative ending.

Does حارا refer to physical heat or emotional warmth?

The word حار literally means physically 'hot'. However, just like in English, it is heavily used metaphorically in MSA to mean 'warm', 'enthusiastic', or 'fervent' when applied to emotions, greetings, and welcomes.