Is the noun clause an appositive or object complement? Is there any rule or test to identify the noun clause as appositive or object complement?
I have often declared the problem that most students do not understand grammar.
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I have often declared the problem [that most students do not understand grammar].
Preliminary points: there is no such thing as a noun clause, and clauses can't function as object complements or appositives. Only NPs can be appositives, and only NPs and AdjPs can be object complements.
In your example the expression "that most students do not understand grammar" is a declarative content clause functioning as complement to the noun "problem".