Через два часа загар на руках стал заметнее, чем утром.

No. Через два часа means two hours later / in two hours / after two hours have passed.

So in this sentence, it sets a later point in time: after two hours, the tan was more noticeable.

By contrast, за два часа usually means within two hours or in the course of two hours, often with the idea of completing something during that span.

Compare:

• Через два часа он вернулся. = He came back two hours later.
• Он сделал это за два часа. = He did it in two hours.

So here через is the correct choice because the sentence is talking about what the situation was like at a point two hours later.

Because через takes the accusative case, and time expressions with numbers follow Russian counting rules.

In через два часа:

• два is in the accusative
• часа is the form used after 2, 3, 4 in nominative/accusative counting expressions

This is the normal pattern:

• через один час
• через два часа
• через три часа
• через четыре часа
• через пять часов

So два часа is exactly what you should expect after через.

Because загар means tan as a general substance/result, not separate tans on each hand.

Russian treats it as one overall thing: the tan on the hands.

That is similar to English, where we also normally say the tan on his hands, not the tans on his hands.

So:

• загар на руках = the tan on the hands
• not загары на руках, which would sound very unnatural here

На руках is prepositional case plural.

Here на means on, in the sense of location, so it takes the prepositional:

• на руке = on the hand
• на руках = on the hands

This is different from motion toward something. If you were talking about putting something onto the hands, you could get the accusative instead:

• нанести крем на руки = to apply cream onto the hands

But here there is no movement. It is simply describing where the tan is located, so на руках is correct.

It can technically mean either, because рука in Russian can refer to the arm/hand more broadly than English hand does.

In this sentence, though, на руках usually means something like on the hands/arms, depending on context. If the meaning shown to the learner says hands, that is a perfectly reasonable translation. But Russian itself is a little broader here than English.

If someone wanted to be very specific about just the hands, they might use кисти рук in some contexts, but that would sound much more specific and less natural in an everyday sentence like this.

Because стал comes from стать, which here means to become.

So:

• стал заметнее = became more noticeable
• был заметнее = was more noticeable

The sentence is describing a change over time. After two hours, the tan had become more noticeable than it was in the morning. That idea of change is exactly why стал is used.

This is a very common Russian pattern:

• стало лучше = it became better
• она стала спокойнее = she became calmer
• цвет стал ярче = the color became brighter

Заметнее is the comparative form of заметный: more noticeable.

In Russian, the simple comparative form does not agree in gender, number, or case with the noun it describes. That is why it stays the same.

Compare:

• загар стал заметнее = the tan became more noticeable
• пятна стали заметнее = the spots became more noticeable
• линия стала заметнее = the line became more noticeable

In all of these, заметнее stays the same.

Russian also has a longer comparative pattern with более:

• более заметный
• более заметным
• etc.

But in a sentence like this, the simple comparative заметнее is the most natural choice.

Чем means than in comparisons.

The full idea is:

• стал заметнее, чем [он был] утром

In other words, Russian leaves out words that are understood from context. The sentence does not need to repeat загар or был.

So чем утром means:

• than in the morning
• more literally, than [it was] in the morning

This kind of omission is very common and natural in Russian.

Because утром is a standard adverbial form meaning in the morning.

It is historically the instrumental case, but in modern Russian learners usually just memorize it as a fixed time expression:

• утром = in the morning
• днём = during the day
• вечером = in the evening
• ночью = at night

So чем утром means than in the morning.

You do also see с утра in Russian, but that means something more like since morning / from the morning onward, which is a different idea.

Russian often omits possessive words with body parts when the owner is obvious or unimportant.

So загар на руках can naturally mean:

• the tan on his hands
• the tan on her hands
• the tan on my hands
• the tan on the hands

The exact owner comes from context.

English usually prefers an explicit possessive more often, but Russian does not always need one. Adding a possessive is possible if needed:

• загар на его руках
• загар на её руках
• загар на моих руках

But without such context, the bare phrase is normal.

Yes, Russian word order is flexible.

The sentence starts with Через два часа to set the time frame first: two hours later...

Then it introduces the subject:

• загар на руках

Then the change:

• стал заметнее

Then the comparison:

• чем утром

This order is very natural because it moves from time to topic to result.

Other orders are possible, for example:

• Загар на руках через два часа стал заметнее, чем утром.

That also works, but it puts slightly less emphasis on the time expression at the start.

So the original order is not the only possible one, but it is smooth and idiomatic.

It means that it was more noticeable after two hours, not necessarily that it was invisible before.

That nuance comes from заметнее, which is a comparative:

• заметный = noticeable
• заметнее = more noticeable

So the sentence suggests a degree of change, not an all-or-nothing change.

If Russian wanted to emphasize that it became noticeable for the first time, it might say something like:

• стал заметен = became noticeable
• стал хорошо заметен = became clearly noticeable

But стал заметнее specifically means became more noticeable.

Not exactly.

Загар means tan: skin becoming darker from the sun.

Sunburn is different. That would usually be expressed with words related to burning, for example:

• солнечный ожог = sunburn
• обгореть на солнце = to get sunburned

So in this sentence, загар refers to tanning, not burning.