I was completely wondering this! If you are friendly with someone than तुम्हारा might be acceptable but in most situations you would use आपका...
I actually posted a complaint on a problem that did not accept आपका as an answer choice! तेरा would be considered rude if you said it to anyone but a child or your significant other! Why are we being taught this first!
In Punjabi (a language which is very similar to Hindi, shares a lot of the same words), the "h" is not pronounced in nahīṅ (although the two words are spelled identically).
Consider: 1) Punjabi is one of the major languages / speech populations in Delhi.
And nor does that mean people consider Delhi to be a mixed or "impure" environment for Hindi. On the contrary, Delhi is routinely cited as the basis for a "khaṛī bolī" (standard speech).
2) Indian regional languages shade into one another. You've got a whole area to the Northwest that is considered to be some or other variety of "Punjabi" which, by the time you move southeast to Delhi, is supposed to be some or other variety of "Hindi." Where is the "border" between the dialects?
It seems possible, even likely, that around Delhi you'll find many people who are speaking Hindi with their Punjabi accent (omitting the H) or who are speaking Hindi with an accent that indeed exists somewhere along the SPECTRUM of regional language.
This is the exact same thing I am getting at with the dropping of auxiliary "hai" in negative constructions in present habitual and progressive tense. One always does that in Punjabi. The authorities say that one "often" does that in Hindi. emrys29, resident of a Hindi speaking area, says one "rare"-ly does it in Hindi. It's possible we could resolve this if we knew whether in, say, Bhopal, Hindi speakers are not under the influence of these things at all, as oppose to Delhi, where if you go there you will probably hear that range of pronunciation.
That is extremely useful information! In fact, as a general trend, as you start from the western and move towards the eastern parts of the Hindi speaking regions (known as the Hindi belt) in India, the ह becomes more and more emphasised, from almost neglected pronunciation in Punjab to a heavy pronunciation in Bihar. :D
You'll get it! Maybe try to say "dog-house," and focus on the sound combining "g-h" in that word. Or, think about the Hindi sound kh ख. It's the exact same sound as the "c" in English "cat." Then think about adding "voicing", i.e. a vibration of the vocal chords, to that sound. The only difference between kh ख and घ is that the first is unvoiced and the second is voiced.