Þær hjálpa hvor annarri að hengja þvottinn á þvottagrindina.

Because þær means they for an all-feminine group.

Icelandic has gendered third-person plural pronouns:

• þeir = they (masculine or mixed group)
• þær = they (feminine group)
• þau = they (neuter, or sometimes for things/children depending on context)

So this sentence tells you the people being talked about are feminine.

Hjálpa is the present-tense plural form, agreeing with þær.

Here it means they help. A useful mini-pattern is:

• ég hjálpa = I help
• þú hjálpar = you help
• hún hjálpar = she helps
• þær hjálpa = they help

So even though hjálpa is also the dictionary form to help, here it is the finite verb help because the subject is þær.

Hvor annarri is the reciprocal expression meaning each other / one another.

In this sentence, it is used because the action is mutual: the women help one another.

A very important point is that hjálpa takes the dative case in Icelandic:

• að hjálpa einhverjum = to help someone

Because of that, the reciprocal phrase also appears in the dative, giving hvor annarri here.

That is normal in Icelandic reciprocal expressions.

Even though the meaning is plural overall, the structure is built with forms that are singular in shape, something like each to the other rather than a straightforward plural form.

So:

• Þær hjálpa hvor annarri = They help each other

The idea is mutual action between members of the group, not a literal singular person.

Because að hengja is the infinitive phrase telling you what they are helping each other do.

So the structure is:

• hjálpa einhverjum að gera eitthvað
  = help someone to do something

Here:

• hjálpa hvor annarri = help each other
• að hengja þvottinn... = to hang the laundry...

The að here is the infinitive marker, like English to.

Because hengja is the transitive verb: it means to hang something.

• hengja = hang something
• hanga = be hanging, hang in the sense of already being suspended

So in this sentence, they are actively putting the laundry up, which requires hengja.

Compare:

• Þær hengja þvottinn. = They hang the laundry.
• Þvotturinn hangir á grindinni. = The laundry is hanging on the rack.

Þvottinn is the definite accusative singular form of þvottur.

It has two things going on:

1. Accusative case
   because it is the direct object of hengja

   • they hang what? → þvottinn

2. Definite article
   Icelandic usually adds the to the end of the noun

   • þvottur = laundry / washing
   • þvottinn = the laundry

So þvottinn means the laundry in the form required by the sentence.

Because á can take different cases depending on whether there is movement or location.

• accusative after á = motion onto something
• dative after á = being on something

Here, the laundry is being hung onto the drying rack, so Icelandic uses the accusative:

• á þvottagrindina

If you were describing where it already is, you would use the dative:

• Þvotturinn er á þvottagrindinni. = The laundry is on the drying rack.

That is one of the most basic features of Icelandic grammar: the definite article is usually a suffix, not a separate word.

So instead of a separate word like English the, Icelandic often does this:

• þvottur → þvotturinn
• þvott → þvottinn
• þvottagrind → þvottagrindin
• þvottagrind in accusative definite → þvottagrindina

In this sentence:

• þvottinn = the laundry
• þvottagrindina = the drying rack

Without the definite article, the meaning would be more like laundry and a drying rack, depending on context.

Because hvor annarri belongs directly with hjálpa as its object/complement, while að hengja... is the infinitive phrase explaining the action they are helping with.

So the sentence is structured like this:

• Þær = subject
• hjálpa = finite verb
• hvor annarri = the person(s) being helped, in a reciprocal sense
• að hengja þvottinn á þvottagrindina = what they help each other do

This is the most neutral, natural order. Icelandic word order can be flexible, but this version is the straightforward one.

The two most important ones are:

• þ = unvoiced th, like in thing
• ð = voiced th, like in this
  though in some positions it can sound weaker than English speakers expect

So in this sentence:

• Þær starts with th
• þvottinn also starts with th
• að has ð, a soft voiced th

A few extra pronunciation notes:

• æ in Þær is roughly like the vowel in eye
• double consonants like tt are held a little longer
• Icelandic stress is usually on the first syllable

So Þær hjálpa hvor annarri að hengja þvottinn á þvottagrindina should sound much more rhythmic and first-syllable-stressed than an English speaker might first assume.