Do we pronounce the "h" in this particular case?

Dropping it is dialectal. I wouldn't.

This is purely dependent on accent. If you're new to the language, always pronounce it.

As an American, it depends on how fast you're speaking.

Only drop it if you're Eliza Doolittle.

you're supposed to say it when you speak the language a lot, and fast, it starts sounding like "is", but it's better to practice saying it with the h

Some people will, some people wont

As a native speaker of American English, I would always pronounce the H, but if I were speaking quickly, it might not be as aspirated. Regardless, the weaker "H" wouldn't be intentional; I'd always aim for pronouncing it.

The overwhelming majority of English dialects would pronounce the H. Some dialects do not, but the vast, VAST majority do.

In full speed speech, yes, I would drop the "h". But if I'm speaking intentionally slowly or putting stress on the word, then the "h" would be pronounced.

I absolutely would, depending on who I'm talking to, how I feel at that specific moment, and how quickly I am saying that sentence. In "proper" English, though, you wouldn't.

As others have said, it varies by dialect and speaker. Personally, I would pronounce the /h/, particularly if *his* is emphasized, like in “I was going in *his* direction” (and not somebody else’s direction).

Drop if spoken quickly. euh-wuzgoin'niz direction But as a rule and if learning no, don't drop it it'll sound weird.

I don’t but I’m American with the standard west coast accent.

where I’m from, it’s dependent on speed if you’re speaking slowly and/or emphasizing the “his” (that is, if it was a question about whose direction we were going), then pronounce the H If speaking fast, then no (“it was goinginis direction”)

Pronouncing the "h" is correct. However, it's very dialectal and you will notice that many native speakers will drop the "h" in casual speech.

Depends on how you would like to pronounce it. If you are native speaker for sure you will be pacing and shall not pronounce 'h'

For an American accent, no you don't. If someone is speaking quickly, the H might be hard to hear but I have always heard it pronounced.

The H is dropped when speaking quickly, but the remaining /ɪ/ in "his" retains the breathiness from the dropped H. Most native speakers don't realize this, hence the answers you're getting. They think they're still hearing the h because the vowel retains breathy voice. They probably imagine only some stereotypical low-class English person would drop the H, but in reality many (most?) accents drop it from pronouns preceded by consonants in rapid speech.

I would drop it, yes, in casual speech: "It was gone (read to rhyme with cone) nen is direction"

Some dialects may drop the h, but, that h is so common that it tends to get written as " 'is " with an apostrophe to specifically note that the h is being left out. The h is very rarely still there, but left silent.

It depends on the dialect. Usually, no, though.

A native speaker in particular cases might sound like, “It was going iniz direction,” but if a learner were to do it intentionally it could very easily sound odd or unnatural.

Only if you are playing a cockney child in a play. “Oh yes governor, it was going in ‘is direction it was, I swear it”

it doesn't really matter

I have a Californian accent, and we tend to speak faster and omit the less important letter sounds in a word. Reading that sentence out loud, I pronounced the “h” but I said it a bit faster and the “h” was one of the first letters to go. For me saying it fast, it sounded like “it was goin innis direction”

Not normally, no. There will be regional or dialectical variations, but as a standard/default, no characters in this sentence would be dropped. Now, in the real world, some people will speak fast, or with varying accents, etc, and some characters can end up dropping, or sounding like they drop, but it is not an intentional rule.

For me, I omit it if I'm talking really fast.

Australian here, I would never pronounce his as is...

Generally no, but it will vary a bit by regional accent. Pick an accent you want to emulate and go with that.

In textbook English, you always pronounce it. Some accents will drop the h, but it’s not the norm.

I always pronounce the hs

Mostly no, but some dialects/accents don’t pronounce h’s at the start of words. Where I live, nobody does, but this will depend depending on what country or even what region you’re in

only in deep english accents. same type of person i imagine says gov'na (more than once in their life)

If you need to ask, don't drop it.