Je mets un peu de crème sur mes mains parce que mes ongles sont très secs.

Because the subject is je.

The verb is mettre (to put / to apply), and in the present tense it changes like this:

• je mets
• tu mets
• il/elle/on met
• nous mettons
• vous mettez
• ils/elles mettent

So je mets means I put / I am putting / I apply.

Yes, mettre literally means to put, but in French it is also very natural for things like putting on cream, lotion, makeup, etc.

So je mets de la crème can mean:

• I put some cream on
• I apply cream

In English, apply may sound more natural in some contexts, but French often uses mettre in everyday speech.

Un peu de means a little (bit) of or some.

So:

• un peu de crème = a little cream
• un peu d’eau = a little water

It is a very common expression for an unspecified small quantity.

After expressions of quantity like un peu de, French normally uses de, not the full partitive article.

Compare:

• Je mets de la crème. = I put on some cream.
• Je mets un peu de crème. = I put on a little cream.

Once you use a quantity expression such as:

• beaucoup de
• un peu de
• trop de
• assez de

you usually use de before the noun.

Sur means on.

So sur mes mains means on my hands.

French uses sur here because the cream is being placed on the surface of the hands. This matches English quite closely.

French usually uses a determiner before a noun, so mains by itself would sound incomplete here.

Mes mains means my hands, and it is very natural because the speaker is talking about their own hands.

French can also sometimes use les with body parts, especially with reflexive verbs:

• Je me lave les mains. = I wash my hands.

But here the sentence is not reflexive, so mes mains is perfectly natural.

Both can mean because, but they are used a little differently.

• parce que is the most common, neutral, everyday way to say because
• car is a bit more formal or literary, and often sounds more like for in English

So in normal spoken or everyday written French, parce que is the most natural choice here.

Because ongles is masculine plural.

• singular: un ongle = a nail
• plural: des ongles = nails

The adjective sec (dry) has to agree with the noun:

• masculine singular: sec
• feminine singular: sèche
• masculine plural: secs
• feminine plural: sèches

Since ongles is masculine plural, French uses secs.

Très is used to intensify adjectives and adverbs.

• très secs = very dry

Beaucoup usually modifies verbs or nouns, not adjectives in this way.

So:

• mes ongles sont très secs = correct
• mes ongles sont beaucoup secs = not correct

Yes. Un ongle can mean a fingernail or a toenail.

Usually the context tells you which one is meant. In this sentence, because the speaker is putting cream on their hands, it is understood that ongles means fingernails.

Because the speaker is talking about both hands and the nails on them in a general way.

• mes mains = my hands
• mes ongles = my nails

French often uses the plural naturally in situations like this, just as English does.

Yes.

The French present tense often covers both:

• the simple present: I put
• the present progressive: I am putting

So Je mets un peu de crème... can mean:

• I put a little cream...
• I’m putting a little cream...

The exact meaning depends on context.

A careful pronunciation would be approximately:

zhuh may uh(n) puh duh krem syur may ma(n) parskuh may zongl suh(n) tray sek

A few useful notes:

• Je sounds like zhuh
• mets sounds like may
• un has a nasal vowel
• crème sounds close to krem
• mes ongles has a liaison, so it sounds like may-zongles
• sont is usually pronounced son here
• secs is pronounced sek

Yes, you could, and it would be understood.

• J’applique de la crème = I apply cream

But in everyday French, mettre de la crème is often more common and more natural in casual speech.

So:

• Je mets un peu de crème sur mes mains = very natural, everyday
• J’applique de la crème sur mes mains = correct, slightly more formal or deliberate

Because crème is part of the quantity phrase un peu de crème.

The full chunk is:

• un peu de crème = a little cream

Here, de links the quantity expression to the noun. You do not add la after un peu de.

So:

• un peu de crème = correct
• un peu de la crème = only possible in special cases, for example if you mean a little of the cream from a specific cream already mentioned

It is perfectly understandable and grammatically correct, and it sounds quite natural.

A native speaker might also say slightly more casual versions, such as:

• Je mets un peu de crème sur les mains parce que j’ai les ongles très secs.
• Je me mets un peu de crème sur les mains parce que j’ai les ongles très secs.

But the original sentence is absolutely fine for normal French.