Mit dem Dynamo leuchtet das Rücklicht hell.

Because mit always takes the dative case in German.

• der Dynamo = the dynamo (nominative)
• dem Dynamo = with the dynamo (dative)

So:

• mit dem Dynamo = with the dynamo

This is one of the most important case rules to memorize: mit + dative.

Das Rücklicht is in the nominative case because it is the subject of the sentence — it is the thing doing the action of leuchtet.

Even though it comes after the verb here, it is still the subject.

A good way to see that is:

• What is shining/glowing brightly?
• Das Rücklicht.

So das Rücklicht is nominative singular.

German main clauses usually follow the verb-second rule (V2). That means the finite verb must be in the second position.

Here, the sentence starts with a prepositional phrase:

• Mit dem Dynamo = first position

So the conjugated verb must come next:

• leuchtet = second position

Then the subject comes after that:

• das Rücklicht

So the structure is:

• Mit dem Dynamo | leuchtet | das Rücklicht | hell

This is normal German word order.

Grammatically, yes, but it sounds less natural in many contexts.

The most neutral version would be:

• Das Rücklicht leuchtet mit dem Dynamo hell.

But German often moves an element like mit dem Dynamo to the front if the speaker wants to highlight it:

• Mit dem Dynamo leuchtet das Rücklicht hell.

So the given sentence puts special focus on with the dynamo.

Leuchtet is the 3rd person singular form of leuchten.

• leuchten = to shine, to glow, to give off light

Here:

• das Rücklicht leuchtet = the rear light shines / lights up / glows

It does not mean to illuminate something in the sense of shining on an object. For that, German often uses other verbs such as beleuchten.

Because hell is not being used before a noun here. It is used predicatively/adverbially, describing how the rear light shines.

Compare:

• ein helles Rücklicht = a bright rear light
  
  • here the adjective comes before the noun, so it gets an ending
• Das Rücklicht leuchtet hell = the rear light shines brightly
  
  • here hell has no ending

So in this sentence, hell works like brightly in English.

You can think of it as an adjective used adverbially/predicatively.

German does not usually add a special -ly ending the way English does. So the same basic form can often mean either:

• bright or
• brightly

In this sentence, hell describes the manner or quality of the shining, so in English you would usually translate it as brightly.

Rücklicht is a compound noun:

• Rück- = rear / back
• Licht = light

So it literally means rear light or tail light.

German uses lots of compound nouns, and this is a very common pattern.

Because Rücklicht is a neuter noun:

• das Rücklicht

Many German nouns have grammatical gender, and the article must match that gender.

Here are the forms of the noun in singular:

• das Rücklicht = nominative
• des Rücklichts = genitive
• dem Rücklicht = dative
• das Rücklicht = accusative

In this sentence it is nominative, so das is correct.

A Dynamo is a device that generates electricity mechanically, traditionally on a bicycle, to power lights.

So mit dem Dynamo means that the rear light is shining using the dynamo or with power from the dynamo.

Depending on context, a natural English translation might be:

• With the dynamo, the rear light shines brightly.
• Using the dynamo, the rear light shines brightly.
• The rear light shines brightly when powered by the dynamo.

Here it expresses means/instrument — the thing used to make the action possible.

So it means something like:

• by means of the dynamo
• using the dynamo
• with the dynamo

This is a very common use of mit in German.

Because leuchten is usually an intransitive verb in this meaning. That means it does not take a direct object.

So in:

• Mit dem Dynamo leuchtet das Rücklicht hell.

there is no direct object. The parts are:

• Mit dem Dynamo = prepositional phrase
• leuchtet = verb
• das Rücklicht = subject
• hell = predicate/adverbial description

A useful check is this: if something leuchtet, it itself is shining. That makes it the subject.

German often puts the most important or contextually relevant information first. The first position in a main clause is flexible.

By starting with Mit dem Dynamo, the speaker may be emphasizing the contrast, for example:

• with the dynamo, the rear light shines brightly
• without it, maybe it does not

So the fronted phrase gives the sentence a particular focus, while still following normal German grammar.

Sometimes learners think of durch because English often uses through or by. But here mit is the more natural choice.

• mit dem Dynamo = using the dynamo / with the dynamo

Durch den Dynamo would suggest something more like through the dynamo or because of the dynamo, and it would sound less natural in this simple instrumental meaning.

So for the intended meaning, mit dem Dynamo is the best choice.