Translation:talking with my father in the afternoon
Both "talking with" and "talking to" are perfectly valid American English. Some people like to maintain a distinction where "talking with somebody" is when you both talk in good faith with no motive but entertainment or sharing information, whereas "talking to somebody" is when you dominate the conversation and use it as an attempt to resolve an issue you have with the other party.
I don't like talking with my father = I don't like chatting with him about random things.
I don't like talking to my father. = I don't like resolving conflicts with him through confrontation.
I would half-agree with DuiliodeAl. I'd say it's more natural to use "to" after the verb "talk", but nowadays people sometimes feel that using the preposition "to" sounds, as tsuj1g1r1 said, too much like "talking at", so they, wrongly in my opinion, correct it to "with". And I have to admit I too am sometimes guilty of that. But of course tsuj... is referring to American English, while I am English English, so there may be a difference. But I bet the Americans and the English have the same hypersensitivity to using "to" in this context.
I thought about translating that phrase as "in the afternoon," but the literal translation is "after noon" which in English could mean any time at all after noon -- it could be that evening, or that night or next Tuesday. So is my translation -- talking with my father after noon -- wrong or just not preferred?
"ba3da DH-DHuhr" usually refers to a specific time, just like "afternoon."
That said, in Arabic, people often use the five daily Islamic prayer times to divide the day into periods:
فَجْر = dawn = about 1am to 8am-ish
ظُهْر = noon = about 11 am to 2 pmish
عَصْر = afternoon or evening = 3 pm to 6 pmish
مَغْرِب = dusk = 6pm to 8pmish
عِشَاء = evening/early night = 8pm to 12 amish
The time values here are only approximations, but it's meant to show that with these words, it can be hard to find an exact match when translating to English. 3asr can be translated as both "evening" and "afternoon," because we just divide the time differently.