Dankzij jouw uitleg begrijp ik het nu helemaal.

Dankzij means thanks to or because of.

In this sentence, Dankzij jouw uitleg means Thanks to your explanation.

A useful nuance:

• dankzij usually has a positive effect
• for a neutral or negative cause, Dutch often uses door

Examples:

• Dankzij jou ben ik op tijd. = Thanks to you, I’m on time.
• Door de file kwam ik te laat. = Because of the traffic jam, I was late.

So here dankzij fits well, because the explanation helped.

Both jouw and je can mean your.

The difference is mainly emphasis:

• je uitleg = your explanation, neutral
• jouw uitleg = your explanation, with extra stress or contrast

So Dankzij jouw uitleg sounds a bit more personal or emphatic, as if the speaker really wants to credit you.

In many situations, Dankzij je uitleg would also be completely natural.

Because jouw already functions as a possessive determiner.

In Dutch, just like in English, you normally do not combine a possessive with an article:

• de uitleg = the explanation
• jouw uitleg = your explanation

Not:

• de jouw uitleg

So jouw replaces the article.

Yes. Uitleg is a noun here, meaning explanation.

Compare:

• uitleg = explanation
• uitleggen = to explain

So:

• Dankzij jouw uitleg... = Thanks to your explanation...
• Dankzij dat jij het uitlegt... = Thanks to the fact that you explain it...

In your sentence, uitleg is the thing being referred to: the explanation itself.

This is because Dutch uses inversion when something other than the subject comes first.

The sentence starts with:

• Dankzij jouw uitleg

Since that element is placed first, the finite verb must come next:

• Dankzij jouw uitleg begrijp ik het nu helemaal.

Basic word order without that fronted phrase would be:

• Ik begrijp het nu helemaal dankzij jouw uitleg.

So:

• first position: Dankzij jouw uitleg
• second position: begrijp
• then subject: ik

This is a very common Dutch word-order rule.

Het means it, and it is the object of begrijp.

Dutch often keeps an object like het where English might sometimes leave it more vague.

Here, het refers to whatever is being understood:

• the topic
• the explanation
• the problem
• the idea

So the sentence is literally:

• Thanks to your explanation, I understand it now completely.

Without het, the sentence would usually sound incomplete:

• Ik begrijp nu helemaal is not natural in this meaning

You normally need:

• Ik begrijp het nu.
• Ik begrijp het nu helemaal.

Nu means now.

It shows a contrast with the earlier situation:

• before: I didn’t understand it
• now: I do

So nu is important because it suggests progress:

• begrijp ik het = I understand it
• begrijp ik het nu = I understand it now

It often implies:

• finally
• at this point
• after your explanation

Here helemaal means something like:

• completely
• fully
• totally

So ik begrijp het nu helemaal means:

• I understand it completely now
• I fully understand it now

A useful thing to know is that helemaal has several uses in Dutch. For example:

• helemaal goed = completely fine / absolutely fine
• helemaal niet = not at all
• Ik begrijp het helemaal. = I understand it completely.

In your sentence, it strengthens begrijp.

Yes, absolutely.

That version is also correct:

• Ik begrijp het nu helemaal dankzij jouw uitleg.

The difference is mainly focus:

• Dankzij jouw uitleg begrijp ik het nu helemaal.
  Focuses first on the cause: thanks to your explanation
• Ik begrijp het nu helemaal dankzij jouw uitleg.
  Starts with the main statement: I understand it now

Dutch is flexible about moving elements, but moving them changes what gets emphasis.

Yes, you can, but it changes the tone a little.

• Dankzij jouw uitleg = thanks to your explanation
  This sounds appreciative and clearly positive.
• Door jouw uitleg = because of your explanation / through your explanation
  This is more neutral.

Since the speaker is expressing a positive result, dankzij is the most natural choice.

So:

• Dankzij jouw uitleg begrijp ik het nu helemaal. = very natural
• Door jouw uitleg begrijp ik het nu helemaal. = possible, but less warm/appreciative

Yes.

Dankzij je uitleg begrijp ik het nu helemaal. is perfectly natural Dutch.

The difference is small:

• je uitleg = neutral, everyday
• jouw uitleg = a bit more emphatic, as if stressing that your explanation made the difference

In speech, both are common. If you are just speaking casually, je is often enough.

It is informal to neutral, mainly because of jouw.

If you are talking to someone formally, you would usually use uw:

• Dankzij uw uitleg begrijp ik het nu helemaal.

So:

• jouw / je = informal singular
• uw = formal singular, and sometimes plural polite

The rest of the sentence is neutral and works in many contexts.

It depends on what you want to emphasize.

Common possibilities:

• DÁNKZIJ jouw uitleg begrijp ik het nu helemaal.
  Emphasis on the cause

• Dankzij JOUW uitleg begrijp ik het nu helemaal.
  Emphasis on your explanation, perhaps contrasting with someone else’s

• Dankzij jouw uitleg begrijp ik het NU helemaal.
  Emphasis on now—I didn’t before

• Dankzij jouw uitleg begrijp ik het nu HELEMAAL.
  Emphasis on full understanding

So the sentence is flexible, and the stress changes the nuance rather than the basic meaning.