Terrenggraden påvirker valget av geocache.

Because terrenggraden is the definite singular form: the terrain rating/grade.

• en terrenggrad = a terrain rating
• terrenggraden = the terrain rating

In Norwegian, definiteness is usually added as a suffix to the noun:

• masculine nouns often take -en
• feminine often -a
• neuter often -et

So terrenggrad + -en = terrenggraden.

In this sentence, the speaker is referring to the terrain rating as a specific factor, so the definite form is natural.

For the same reason: valget is the definite singular form of valg.

• et valg = a choice
• valget = the choice

So:

• Terrenggraden påvirker valg would sound more general or incomplete
• Terrenggraden påvirker valget means the terrain rating affects the choice

Here, valget refers to the specific choice someone makes.

Påvirker is the present tense of the verb å påvirke = to affect / influence.

• å påvirke = to affect
• påvirker = affects / is affecting

Norwegian present tense is quite simple. The verb does not change for person:

• jeg påvirker = I affect
• du påvirker = you affect
• den påvirker = it affects

So in this sentence:

• Terrenggraden påvirker valget av geocache.
• The terrain rating affects the choice of geocache.

It follows normal Norwegian subject–verb–object order:

• Terrenggraden = subject
• påvirker = verb
• valget av geocache = object phrase

So literally:

• The terrain rating / affects / the choice of geocache

This is a very standard declarative sentence pattern in Norwegian.

Because valg av X is a common Norwegian pattern meaning choice of X or selection of X.

So:

• valg av geocache = choice of geocache
• valg av bil = choice of car
• valg av klær = choice of clothes

Here, av works much like English of in this kind of noun phrase.

It is not mainly about possession. It is about what is being chosen.

Because after valg av, Norwegian often uses a noun without an article when speaking in a general sense.

So:

• valg av geocache = choice of geocache / choice of which geocache to pick

This is similar to other Norwegian phrases such as:

• kjøp av bil = purchase of a car / purchase of cars
• bruk av mobiltelefon = use of a mobile phone / use of mobile phones

The bare noun often sounds more natural in these abstract constructions.

You could sometimes see valg av en geocache, but that would usually feel more specific and less natural in a general statement.

Formally, it is singular in form, but in this kind of construction it often has a general meaning.

So valg av geocache can mean something like:

• the choice of geocache
• the choice of which geocache to select
• geocache choice in general

Norwegian often uses a bare singular noun in abstract phrases where English may also sound general.

It is basically a loanword from English, used in Norwegian because geocaching is an international hobby.

In Norwegian, people often still use forms like:

• en geocache
• geocachen
• geocacher (plural)
• geocachene (definite plural)

So even though the word comes from English, it can behave like a Norwegian noun in everyday usage.

Not naturally in most normal contexts.

Norwegian usually prefers the definite forms here:

• Terrenggraden påvirker valget av geocache.

That sounds like a complete, idiomatic statement: The terrain rating affects the choice of geocache.

If you remove the definite endings:

• Terrenggrad påvirker valg av geocache

it starts to sound more like a heading, note, label, or very compressed style rather than an ordinary sentence.

In geocaching, terrenggrad refers to the terrain rating: how physically difficult it is to reach the cache.

It is a compound noun:

• terreng = terrain
• grad = grade / level / degree

So terrenggrad literally means something like terrain grade.

Norwegian forms compound nouns very freely, so this kind of word is very normal.

A few natural paraphrases are:

• The terrain rating affects the choice of geocache.
• The terrain rating influences which geocache is chosen.
• The terrain difficulty affects which geocache people choose.

The Norwegian sentence is compact and neutral, and these English versions capture that well.

They are similar in meaning, but the style is different.

• valget av geocache = the choice of geocache
  
  • more compact
  • more formal or informational
• hvilken geocache man velger = which geocache one chooses
  
  • more explicit
  • slightly more conversational

So:

• Terrenggraden påvirker valget av geocache.
• Terrenggraden påvirker hvilken geocache man velger.

Both are correct, but the original sentence is a bit more concise and formal in tone.