The clip is very muffled so it's hard to hear. There seems to be some disagreement on whether the "h" is pronounced or not. Listen to the 7 pronunciations HERE. Some of the speakers pronounce it and some don't. I don't.

Student or Learner
How do you say 'prohibition'?
Is the sound 'h' is pronounced or not?
Here's my trial.
https://clyp.it/ywns4zhx
The clip is very muffled so it's hard to hear. There seems to be some disagreement on whether the "h" is pronounced or not. Listen to the 7 pronunciations HERE. Some of the speakers pronounce it and some don't. I don't.
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.
A new streamhttps:
https://clyp.it/wvmtozsb
I thought the Ken Burns documentary Prohibition would be an authoritative source to resolve this queation. It turns out that both peonunciations are used in that series depending on who is speaking. So in AmE both are very acceptable.
I'm pretty sure I say it both ways. I'm more likely to pronounce the /h/ if I'm speaking slowly. I'm not completely sure I ever drop it entirely, but I think it can be so faint as to be barely perceptible.
I am not a teacher.