Komposita.
The last word decides everything.

German loves to glue nouns together, so words that English would split into two or three, German welds into one → Hausaufgabe, Lebensmittel, Kühlschrank, Krankenversicherung. It looks intimidating, but one rule covers almost every long German noun: however many pieces it's built from, only the very last one decides the gender, the plural, and which suffix rule applies.

The rule: the last word wins

A German compound noun is read like a chain, but only the final link matters for grammar. Whatever article and plural the last word would have on its own, the whole compound inherits.

Pieces	Last word	Compound	Meaning
dasHaus + dieAufgabe	dieAufgabe	dieHausaufgabe	homework
kühl + derSchrank	derSchrank	derKühlschrank	fridge
dasLeben + dasMittel	dasMittel	dasLebensmittel	food, groceries
dieZeit + derPunkt	derPunkt	derZeitpunkt	point in time
derKredit + dieKarte	dieKarte	dieKreditkarte	credit card

Notice Hausaufgabe → dasHaus is neuter, but dieAufgabe is feminine, and feminine wins because Aufgabe comes last. The first part, or parts, of a compound only add meaning, and they almost never affect the gender.

Almost, because one old group breaks it and is worth knowing: derMut, but die Armut, die Demut, die Wehmut, die Anmut. Same with der Teil, which turns up as das Urteil and das Gegenteil. These are old formations rather than everyday compounds, and they are the only common exceptions to the rule.

Why this is good news: the suffix rules still apply

Every gender-by-suffix rule you already know still works inside a compound, as long as you look at the last word. If the final piece ends in -ung, -heit, -keit, or -schaft, the whole compound is die. If the last word is a diminutive in -chen or -lein, the whole compound is das. The letters alone are not enough: der Apfelkuchen ends in -chen and stays der, because Kuchen is not a smaller anything. The suffix rule never cares how long the word got on the way there.

Compound	Last word	Suffix rule	Article
Krankenversicherung	Versicherung	ends in -ung	die
Geschwindigkeit	(Geschwind)igkeit	ends in -keit	die
Bürgermeister	Meister	-er agent noun	der
Mädchen	(Mäd)chen	ends in -chen	das

This means every suffix article on this blog applies twice over, once to the simple word and again to every compound that happens to end in it. Learn the rule once, and it keeps paying off on words you've never seen before.

Connector letters: the little extras in between

Sometimes an extra letter or two slips in between the pieces, purely to make the word easier to say. The most common is an extra -s-, often after words ending in -ung, -heit, -keit, -schaft, or -tum. An -(e)s-, an -(e)n- or an -er- can also appear, echoing a Genitiv or plural form of the first word: Huhn borrows its plural Hühner.

Pieces	Connector	Compound	Meaning
dieArbeit + derPlatz	-s-	derArbeitsplatz	workplace
derTag + dieZeit	-es-	dieTageszeit	time of day
dasHuhn + dieSuppe	-er-	dieHühnersuppe	chicken soup

These connector letters never change the rule. They sit quietly in the middle, and the gender still comes from whatever word is last.

Reading a long word from right to left

The longer a German compound gets, the more useful this rule becomes. When you meet a word you've never seen, don't try to take in the whole thing at once. Find the very last word first, since that's the core noun, the one that gets the article and the plural, and then work backwards through the earlier pieces to fill in the meaning.

This is also why the famously enormous German compound words aren't actually hard once you stop reading them left to right. Find the last noun, get its gender and plural for free from a rule you already know, and treat everything before it as a string of labels.

For the suffixes that decide gender on their own: Ends in -ung? It's always die. and Ends in -chen? A diminutive is always das.