I could use some expert advice.

20 horsepower diesel engine turning *a 12 x 14 R/H 3 blade prop, engine runs no load full fuel at 3200 rpm @ 2750 rpm I can cruise at 6.0 knots max speed on a good day is 6.2 knots at 3100 rpm *full fuel. *If I change the prop to a 12x15 or 12x16 will this increase my top speed, I would like to cruise at 6.5 to 7.0 knots, I am not sure if this is possible with my 20 horsepower engine I believe my transmission ratio to be 2.4:1 but I could be wrong on that. *All advise will help. *thank you

No expert here. But....defining factor is your hull design and dimensions.
That said, it looks to me like you're prop'd ok.
Hull speed for a displacement hull under 30' would only be in the 6 kt range. Over prop you're just going to burn more fuel and/or lug your engine.
My non-expert opinion.

One inch of pitch will reduce your WOT RPM about 200 RPM's. What is the max RPM spec for the engine? What RPM are you getting now when you run full throttle?

engine runs no load full fuel at 3200 rpm
@ 2750 rpm I can cruise at 6.0 knots max speed on a good day is 6.2 knots at 3100 rpm full fuel.

Running max load of 3100 with a no load rpm of 3200 is about normal.

Only gaining .2K for over 300 rpm shows you are getting all the speed the hull is capable of .

A far larger engine would be required to go much faster.

Personally I would not cruise above 2700 for long periods of time.

It would be interesting if you would publish a speed/rpm chart , as perhaps a different prop would cruise at the same 6K but at say 2200 , for better engine efficiency and service life.

Sounds like your'e under-proped. One would need to know your gear ratio, displacement and hull design to be able to give anything but guesses. I have lots of experience w small boats like yours and could be of help. Don't over-prop. If your max hp is at 3000rpm then you should get 3000rpm at WOT (wide open throttle). The governor is there and set to 3200 to keep you from over speeding your engine. Max hp should be 2800 to 3000. If your boat is full displacement and 2 or 3 tons 20hp is probably enough power. Let's hear more about your boat and look for a plackard on the gearbox itself for the gear ratio. I ran my Albin w 34hp at 3450rpm (Yanmar) at 2750rpm most of the time but a 3000rpm engine should run 2300 to 2500 rpm most or all of the time. The most important thing is max hp rpm at WOT.

Eric Henning