Engine problem definitions?
 

Hi
1-What is engine flame out?
2-What is engine roll back?
3-What is engine seized?
4-What is engine failure?

Not sure what sort of definition you're looking for but:

Flameout: the flame in the combustion chamber is extinct, caused by a variety of factors e.g. Birds, stall, excessive water consumption
Roll back: the thrust is less than you've requested via the thrust lever but is still producing thrust. Anywhere between less than requested an idle.
Seized: rotational speed of a section of the engine has stopped entirely I.e. isn't windmilling in the airflow as you'd expect in a simple rundown. It signifies damage.
Failure: the engine isn't working. It doesn't differentiate between severe damage or a gentle run down that you may not even notice from the cabin.

I don't know that I'd include birds as a cause of a flameout but that's just me.

Engine failure often includes an engine that can't produce requested thrust by a defined amount, particularly on takeoff power.

1 - just what it sounds like, an inability to maintain combustion.
2 - during start an engine peaks out at a high start temperature then "rolls back" to idle.
3 - mechanical failure that prevents it from rotating
4 - when an engine quits operating or operates un commanded outside of safe limitations

If you ask a 146 mate about Roll Back you'll get a completely different answer.

Makes a difference in how the definitions are used. If you are a pilot doing training on type you better understand the symptoms displayed to you vs the proper check list. Such check lists may have a definition basis quite different from what an engine designer/manucfaturer would use.

I might suggest that flameout is the single most misused/understood acronym between the two (but do you really care as long as you know what to do?)

That followed by surge and stall, but again do you care?

Seizure is another term that does not always mean the same thing. Engines don't seize that just look that way :)

So, the question is interesting but the scenario as asked is important before answering.

Take a look at this link: Turbofan Engine Malfunction Recognition and Response

It's quite general, quite a good read.