HELP WITH GRAMMAR, IDENTIFICATION OF WORDS.

out = preposition
of = preposition
the = adjective (definite article)
mist = noun
stepped = verb
a = adjective (indefinite article)
man = noun
holding = adverb
a = adjective (indefinite article)
vegetable = adjective
omlet - noun.

"Man" is the subject, "stepped" the predicate. "Holding a vegetable omlet" is an adverbial phrase and "out of the mist" is a prepositional phrase.

I wish all homework assignments were as easy as that.

MA-

It looked good but don't ever try it with Proust.

Mais j'aime "Les Temps Perdu."

We spell it omelette
I've never tried a vegetable omelette; are they any good?

So why was there so much mist in the kitchen?

Or was it an early breakfast at Boy Scout Camp?

Just wondering.

my frined went to Reunion Island and he was staying so high up in the mountains that when someone left a door open the morning mist came in and his head was in the clouds when he got up. Maybe the man was in Reunion Island.

From the sentence I would guess that Wendi is studying verbals (infinitives, gerunds and participles). "holding a vegetable omelet" is a participial phrase in which "holding" is a participle (verb used as an adjective).