Met deze uitleg kunnen wij de grammatica eenvoudig begrijpen.

This is because Dutch follows the verb-second rule in main clauses.

In this sentence, Met deze uitleg is placed first. Once something other than the subject comes first, the conjugated verb must come next, and the subject follows it:

• Met deze uitleg = first position
• kunnen = second position
• wij = subject

So:

• Wij kunnen de grammatica eenvoudig begrijpen.
• Met deze uitleg kunnen wij de grammatica eenvoudig begrijpen.

Both are correct, but the word order changes because the sentence starts with a different element.

Yes, absolutely.

That version is also correct and has basically the same meaning. The difference is mainly emphasis:

• Wij kunnen met deze uitleg... puts the subject wij first and sounds more neutral.
• Met deze uitleg kunnen wij... puts focus on with this explanation.

Dutch often moves parts like time phrases, place phrases, or prepositional phrases to the front for emphasis or flow.

Met deze uitleg literally means with this explanation.

Depending on context, it can feel like:

• with this explanation
• using this explanation
• thanks to this explanation

Here met is a preposition meaning with, and deze uitleg is the object of that preposition.

Because uitleg is a de-word.

In Dutch, the demonstratives work like this:

• deze for de-words and plurals
• dit for singular het-words

Since it is:

• de uitleg

you get:

• deze uitleg

If it were a het-word, you would use dit instead.

Uitleg is a noun meaning explanation.

A few useful things about it:

• It is a de-word: de uitleg
• It is singular here
• It can refer to an explanation in general or a specific explanation

It is related to the verb uitleggen, which means to explain, but as a noun it behaves like any other noun.

Because grammatica is a de-word:

• de grammatica

So if you use the noun with an article, it must be de.

In this sentence, de grammatica most naturally means the grammar being discussed, or grammar as the system you are trying to understand. Dutch often uses the article in cases like this where English might or might not use the, depending on style.

Because eenvoudig is functioning as an adverb here, not an adjective before a noun.

It modifies the verb phrase begrijpen:

• eenvoudig begrijpen = understand easily / understand in a simple way

Dutch adverbs often have the same form as the basic adjective:

• een eenvoudige uitleg = an easy/simple explanation
• eenvoudig begrijpen = to understand easily

So there is no -e here.

Because kunnen is a modal verb.

With modal verbs in Dutch, the modal is the conjugated verb, and the main verb usually goes to the end in the infinitive:

• Wij kunnen ... begrijpen
• Ik wil ... leren
• Zij moet ... werken

So in your sentence:

• kunnen = conjugated modal verb
• begrijpen = infinitive main verb at the end

This is very normal Dutch sentence structure.

Yes. Both mean we.

The difference is mainly style and stress:

• we = more common in everyday speech
• wij = fuller form, often used for emphasis, contrast, or slightly more formal style

So these are both possible:

• Met deze uitleg kunnen we de grammatica eenvoudig begrijpen.
• Met deze uitleg kunnen wij de grammatica eenvoudig begrijpen.

In ordinary spoken Dutch, we is often more natural.

It can be understood as either can or are able to. In this sentence, the meaning is basically:

• can understand
• are able to understand

Dutch kunnen often covers both ideas.

Eenvoudig is correct and understandable, and it sounds a bit more careful or formal.

In everyday Dutch, many speakers would more often say:

• makkelijk
• gemakkelijk

So you might also hear:

• Met deze uitleg kunnen we de grammatica makkelijk begrijpen.
• Met deze uitleg kunnen we de grammatica gemakkelijk begrijpen.

All of these are correct. Eenvoudig is slightly more formal or written-sounding than makkelijk.