Your question is not really understood. If you meant to ask which sentence is right, it depends on what you want to say. 1. If you wanted to say something like "I'm glad that you understood", as when you tell something to someone that you were afraid it could cause a problem, but it didn't and the other person was considerate and understood the situation, then the right sentence would be: أنا سعيد أنك تتفهّم/ تفهّمت. 2. If you wanted to say something like you are happy that someone understood, as after they understood a mathematical equation for example, then it's better to say: أنا سعيد أن فهم المعادلة كان سهلًا بالنسبة لك/ أنا سعيد لأنك فهمت المعادلة. So it really depends on the context! I'm not going to ask why you voted or anything! You have to know though that the first sentence isn't correct grammatically and it has no clear meaning. I wish you good luck.

the accurate translation: أنا سعيد انك متفهَم

You should say : أنا سعيد أنّك تفهم The first one is wrong .

I think your question is how to use "التي" versus "أن", which could both be the word "that". However, you're talking about going from English -> Arabic, so you must understand the parts of English grammar in order to correctly chose a word for the Arabic version. In English, we have multiple meanings assigned to the word "that". It can be a conjunction as "He said /that/ Bob likes fish", or it can be a pronoun "I want /that/!", or adjective "I want /that/ cat.". The list goes on, but it isn't helpful to talk about the word "that" alone -- we need context, so let's look at examples. When you have a sentence like "He said that...", "I hope that...", "I'm happy that..." you will virtually always use أن or إن, because what follows is another idea/sentence (or more technically speaking, a subordinate clause). Thus, the answer to your question directly is "أنك should be used". In the second case, التي / الذي (or any of its many forms) is more of "who, which, that", i.e. relative pronouns. For example: "I saw the man /that/ helped my sister" رأيت الرجل الذي ساعد أختي Because the word "man" is masculine and singular, الذي matches it and refers to it.

انا سعيد انك تفهم = correct I'm happy that you understand sentence number 2 you say I'm happy who you understand --- It's wrong التي == who ( famale )