Jeg kan hverken aflæse elmåleren eller finde sikringsskabet.

It means neither ... nor.

So:

• hverken aflæse elmåleren
• eller finde sikringsskabet

together means:

• neither read the electricity meter nor find the fuse box

This is a very common Danish structure for linking two negative alternatives.

Because hverken ... eller already makes the sentence negative.

So Danish says:

• Jeg kan hverken ... eller ...

not normally:

• Jeg kan ikke hverken ... eller ...

That would be unnecessary double negation in standard Danish.

Because kan is the finite verb, and in a normal Danish main clause the finite verb comes early.

The structure is:

• Jeg = subject
• kan = finite verb
• hverken ... eller ... = the two coordinated infinitive phrases

So the sentence pattern is very natural Danish word order:

• Jeg kan hverken X eller Y.

Because they depend on the modal verb kan.

After modal verbs like:

• kan = can
• vil = want/will
• skal = must
• må = may/must

the next verb is usually in the infinitive without at.

So:

• kan aflæse
• kan finde

not:

• kan aflæser
• kan at aflæse

Læse usually means to read in a general sense, like reading a book or reading text.

Aflæse is more specific: it means to read off, take a reading, or read from a meter/instrument/display.

So with elmåleren, aflæse is the natural verb because you are taking the meter reading, not just reading words.

Because Danish often uses the definite form where English would say the.

• elmåleren = the electricity meter
• sikringsskabet = the fuse box / electrical cabinet

The endings show definiteness:

• -en for many common-gender nouns
• -et for many neuter nouns

Here:

• en elmåler → elmåleren
• et sikringsskab → sikringsskabet

Yes. Danish uses compound nouns very often.

• elmåler = el

  • måler
  • el = electricity
  • måler = meter/gauge

• sikringsskab = sikring

  • skab
  • sikring = fuse / protection / circuit protection
  • skab = cabinet / cupboard

So Danish packs a lot of meaning into one word where English often uses several words.

Because one modal verb can govern both infinitives.

So:

• Jeg kan hverken aflæse elmåleren eller finde sikringsskabet.

means:

• I can neither read the electricity meter nor find the fuse box.

Repeating kan is usually unnecessary here. Danish, like English, commonly uses one modal for both parts of the pair.

Yes. On its own, eller usually means or.

But in the pattern hverken ... eller, it corresponds to English neither ... nor.

So although eller by itself is usually or, in this fixed pair the whole expression has a negative meaning.

In a normal full sentence, jeg is necessary.

Danish usually requires an explicit subject in finite clauses:

• Jeg kan ... = correct
• Kan hverken aflæse ... = only possible in special contexts, like a shortened reply, note, or informal message

So in a standard sentence, you need jeg.

You mainly learn noun gender together with the noun:

• en elmåler
• et sikringsskab

That is why the definite forms are:

• elmåleren
• sikringsskabet

There is not always a reliable way to guess gender from meaning alone, so it is best to memorize nouns with en or et from the start.

Yes, it sounds natural.

It is a normal, idiomatic way to say that someone is unable to do either of two things. The sentence is slightly specific because of the vocabulary, but grammatically it is completely everyday Danish:

• Jeg kan hverken X eller Y.

That pattern is very common in speech and writing.