Этот крем помогает увлажнять сухие руки.

Because этот has to agree with крем.

• крем is a masculine singular noun.
• The demonstrative этот means this for a masculine singular noun in the nominative case.

So:

• этот крем = this cream
• эта would be for a feminine noun
• это would be for a neuter noun

Крем is in the nominative case because it is the subject of the sentence — the thing doing the helping.

So the structure is:

• Этот крем = subject
• помогает = verb
• увлажнять сухие руки = what it helps do

Because the subject is этот крем, which is third person singular: it helps.

The verb is помогать = to help.
Its present-tense forms include:

• я помогаю = I help
• ты помогаешь = you help
• он / она / оно помогает = he / she / it helps

Since крем is it, you get помогает.

In Russian, помогать can be followed by an infinitive to mean help to do something.

So:

• помогает увлажнять = helps moisturize / helps to moisturize

This is a very common pattern:

• помогает понять = helps understand
• помогает учиться = helps study
• помогает увлажнять = helps moisturize

Because the sentence describes the cream’s general function or ongoing effect, not one single completed action.

• увлажнять = imperfective, focusing on the process or repeated/general action
• увлажнить = perfective, focusing on a completed result

On product labels or in general descriptions, Russian often prefers the imperfective for this kind of meaning:

• Этот крем помогает увлажнять сухие руки
  = This cream helps moisturize dry hands.

If you used увлажнить, it would sound more like helping achieve a specific completed result in a particular instance.

It is the accusative plural, because it is the direct object of увлажнять.

You moisturize what?
сухие руки

So grammatically it is accusative. However, for inanimate plural nouns, the accusative often looks exactly like the nominative.

That is why:

• nominative plural: сухие руки
• accusative plural: сухие руки

They look the same here.

Because руки is inanimate plural, and in the accusative plural, inanimate nouns and their adjectives usually have the same form as the nominative plural.

So:

• сухие руки = nominative plural
• сухие руки = accusative plural too

If the noun were animate plural, you would often see a different form.

Also, сухие agrees with руки in:

• number: plural
• case: accusative
• gender: plural adjectives do not show separate gender

Because the sentence is talking about hands in general, usually meaning both hands.

So:

• сухие руки = dry hands
• сухую руку = a dry hand / one dry hand

Using the plural here is natural, just like in English: This cream helps moisturize dry hands.

Russian does not have articles like a and the.

So сухие руки can mean:

• dry hands
• the dry hands
• some dry hands

The exact meaning depends on context.

In this sentence, the meaning is general: dry hands as a type of problem the cream helps with.

Yes. Russian word order is fairly flexible, because case endings do a lot of the grammatical work.

The sentence as written is the most neutral, natural order:

• Этот крем помогает увлажнять сухие руки.

That is basically:

• This cream helps moisturize dry hands.

You can move words around for emphasis, but the sentence may sound less neutral or more stylistically marked.

Yes, but that means something slightly different.

• Этот крем для сухих рук = This cream is for dry hands.
• Этот крем помогает увлажнять сухие руки = This cream helps moisturize dry hands.

The first describes the product’s intended use.
The second describes its effect or function.

Both are natural, but they are not exactly the same statement.

Yes, поможет is possible, but it means something a bit different.

• помогает = helps, is helpful, has this function
• поможет = will help

In product descriptions, Russian often uses the present tense to describe what a product generally does:

• Этот крем помогает... = This cream helps...

That sounds like a general property of the cream, which is very natural here.

The stress is:

Э́тот крем помога́ет увлажня́ть сухи́е ру́ки.

A rough pronunciation guide:

• Э́тот = EH-tət
• крем = krem
• помога́ет = pə-ma-GA-yet
• увлажня́ть = oo-vlazh-NYAT'
• сухи́е = soo-KHEE-ye
• ру́ки = ROO-kee

The most important thing for a learner is to notice the stressed syllables, especially in помогает, увлажнять, сухие, and руки.