Nogle ord har en tydelig modsætning, og læreren siger, at en modsætning ofte er lettere at huske end et synonym.

Nogle ord means some words.

• nogle = some
• ord = words / word

You use the bare plural noun after nogle. So nogle ord works just like English some words.

You would not say nogle ordene, because ordene means the words, and that would clash with nogle.

Because modsætning is a common-gender noun in Danish, so it takes en, not et.

That also affects the adjective:

• en tydelig modsætning
• et tydeligt ord would be correct with a neuter noun

So here:

• en = common gender article
• tydelig = adjective form used with an indefinite singular common-gender noun
• modsætning = opposite / antonym

A quick comparison:

• en tydelig modsætning
• et tydeligt eksempel
• tydelige modsætninger (plural)

Here modsætning means an opposite or antonym.

In other contexts, modsætning can also mean:

• contrast
• opposition
• opposite relationship

But in this sentence, because it is compared with synonym, the intended meaning is clearly antonym/opposite word.

So:

• synonym = a word with a similar meaning
• modsætning = a word with the opposite meaning

Læreren means the teacher.

In Danish, the definite article is often added to the end of the noun:

• en lærer = a teacher
• læreren = the teacher

So læreren siger means the teacher says.

This is one of the big differences from English: Danish often marks definiteness with a suffix instead of a separate word.

Because at en modsætning ofte er lettere at huske end et synonym is a subordinate clause.

Main clause:

• læreren siger

Subordinate clause:

• at en modsætning ofte er lettere at huske end et synonym

Danish normally uses a comma before subordinate clauses introduced by words like at, fordi, som, hvis, etc.

So the comma here is very normal in written Danish.

Because Danish subordinate clauses usually place sentence adverbs like ofte before the finite verb.

So in a subordinate clause, this is the normal pattern:

• at en modsætning ofte er lettere...

not

• at en modsætning er ofte lettere...

This is an important Danish word-order rule.

Compare:

• Main clause: En modsætning er ofte lettere at huske.
• Subordinate clause: ... at en modsætning ofte er lettere at huske.

In the subordinate clause, ofte comes before er.

Lettere is the comparative form of let.

• let = easy
• lettere = easier
• lettest = easiest

So er lettere at huske means is easier to remember.

A useful pattern:

• let at forstå = easy to understand
• lettere at huske = easier to remember

Even though let can also mean light in other contexts, here it clearly means easy.

Because Danish often uses adjective + at + infinitive in the same way English uses adjective + to + verb.

So:

• lettere at huske = easier to remember
• svært at forstå = difficult to understand
• nemt at lære = easy to learn

Here:

• at huske = to remember

So the structure is completely natural Danish grammar.

After a comparative like lettere, Danish uses end to mean than.

So:

• lettere ... end ... = easier ... than ...

And synonym is a neuter noun, so it takes et:

• et synonym

That gives:

• lettere at huske end et synonym = easier to remember than a synonym

Danish often uses the indefinite singular to talk about something in a general sense, just like English can.

So en modsætning here does not mean one specific opposite; it means an opposite / an antonym as a type of thing.

This is similar to English sentences like:

• A cat is an independent animal.
• A synonym can be hard to remember.

So en modsætning ofte er lettere at huske means an opposite is often easier to remember, in a general statement.

Yes. Tydelig means clear, distinct, or obvious, depending on context.

In en tydelig modsætning, it means something like:

• a clear opposite
• a distinct contrast
• an obvious antonym

The adjective agrees with the noun:

• en tydelig modsætning
• et tydeligt tegn
• tydelige forskelle

So this is a good example of normal adjective agreement in Danish.

Yes. Literally, it is:

• og = and
• læreren = the teacher
• siger = says

So og læreren siger = and the teacher says

That is a perfectly normal literal translation. Depending on style, English might sometimes phrase things a bit differently, but grammatically this Danish part is very straightforward.