मुझे यह बालकनी पसंद आई।

Because Hindi often uses a dative experiencer pattern for feelings, preferences, and sensations.

With पसंद आना, Hindi does not structure the sentence like I liked X. It structures it more like:

To me, X was pleasing.

So:

• मैं = I as a subject
• मुझे = to me / me

That is why मुझे is the natural form here.

A similar pattern appears in:

• मुझे भूख लगी है। = I am hungry
• मुझे ठंड लग रही है। = I am feeling cold
• मुझे यह किताब पसंद है। = I like this book

Because this is not a मैंने ... type sentence.

The verb here is part of the expression पसंद आना, and the thing liked is treated as the grammatical subject. In this sentence, बालकनी is what the verb agrees with, not मैं.

So Hindi is not saying:

• I did liking to the balcony

It is saying something more like:

• This balcony appealed to me

That is why you get:

• मुझे, not मैंने
• agreement with बालकनी
• no ने

It comes from the expression पसंद आना, which means to be liked, to appeal, or to please someone.

So पसंद आई is not best understood word-by-word in English, even though literally it looks like something like liking came.

The important point is:

• पसंद आना = to be pleasing / to be liked
• पसंद आई = was liked / appealed

This expression is extremely common in Hindi.

Because आई agrees with बालकनी, and बालकनी is feminine singular.

In this construction, the verb agrees with the thing being liked, not with the person who likes it.

So:

• यह बालकनी → feminine singular → आई
• यह कमरा → masculine singular → आया

Compare:

• मुझे यह बालकनी पसंद आई।
• मुझे यह कमरा पसंद आया।

Yes. In Hindi, borrowed words still get grammatical gender, and बालकनी is normally treated as feminine.

That is why you see:

• यह बालकनी अच्छी है।
• मुझे यह बालकनी पसंद आई।

This is very normal in Hindi. Even loanwords usually behave like regular Hindi nouns once they are part of the language.

This is a very useful distinction.

• मुझे यह बालकनी पसंद है = I like this balcony / This balcony is pleasing to me
• मुझे यह बालकनी पसंद आई = I liked this balcony / I found this balcony appealing

A simple way to think about it:

• पसंद है often describes a present or general liking
• पसंद आई often describes your reaction after seeing, visiting, or experiencing it

So if you are looking at an apartment and then say your impression, पसंद आई is very natural.

Yes. Hindi word order is flexible, because endings and postpositions help show the roles of words.

This sentence can also appear as:

• यह बालकनी मुझे पसंद आई।

Both are natural. The difference is mainly one of emphasis or flow.

• मुझे यह बालकनी पसंद आई। puts to me first
• यह बालकनी मुझे पसंद आई। puts this balcony first

English is more rigid about word order than Hindi.

It is written यह, and in everyday speech it is usually pronounced more like yeh.

So learners often hear:

• yeh balcony mujhe pasand aayi

In careful or traditional pronunciation, it may sound closer to yah, but yeh is what you will commonly hear in conversation.

Yes, absolutely. That is a very natural alternative.

• मुझे यह बालकनी पसंद आई। = I liked this balcony
• मुझे यह बालकनी अच्छी लगी। = This balcony seemed nice/good to me

The meanings are close, but not identical:

• पसंद आई focuses more on liking
• अच्छी लगी focuses more on the impression that it seemed good/nice

Both are common and useful.

You add नहीं before the verb part:

मुझे यह बालकनी पसंद नहीं आई।

That means:

• I did not like this balcony
• This balcony did not appeal to me

This is the normal way to negate it.