Answer:
I assume this exercise asks for the translation to English because it asks to fill in the article of the German words and then fill in "deine Sprache" (= your language). They also hint the plural form of the German words, I'm not sure if the exercise wants you to list this as well.
Just in case, I will list the nouns in this format:
singular / plural - english translation in singular
Some words only exist in singular or plural, then I will add this in parenthesis.
Nomen / nouns:
der Ärger - the anger (no plural)
das Bad / die Bäder - the bath ( the word "Bad" also can refer to the bathroom, short for "das Badezimmer")
der Besuch / die Besuche - the visit
die Blume / die Blumen - the flower
der Cousin / die Cousins - the cousin
das Familienfoto / die Familienfotos - the family photo
die Geschwister - the siblings (plural only)
die Großeltern - the grandparents (plural only)
die Großmutter / die Großmütter - the grandmother
der Großvater / die Großväter - the grandfather
der Konflikt / die Konflikte - the conflict
die Küche / die Küchen - the kitchen (also can mean cuisine)
der Mann / die Männer - the man
die Mutter / die Mütter - the mother
die Oma / die Omas - the grandmother (Oma is just a nickname for your grandmother, here you might need to fill in what you call your grandmother: gran / granny / nana etc)
der Onkel / die Onkel : the uncle
der Opa / die Opas - the grandfather (again, a nickname for your grandfather, fill in what you call your grandfather: gramps / granpa etc)
der Papa / die Papas - dad (nickname that you adress your father with)
die Person / die Personen - the person
die Ruhe - the quiet / the silence (singular only)
das Schlafzimmer / die Schlafzimmer - the bedroom
die Tante / die Tanten - the aunt
die Tür / die Türen - the door
der Vater / die Väter - the father
der Verwandte - singular for a male relative
die Verwandte - singular for a female relative
die Verwandten - plural for multiple relatives
die Wohnung / die Wohnungen - the apartment / the condo
das Wohnzimmer / die Wohnzimmer - the livingroom
das Zuhause - the home (singular only)
verbs:
aufmachen - to open
aufräumen - to tidy up
bleiben - to stay
duschen - to take a shower
lassen - to let somethin be / to leave something
mitbringen - to bring something along / to bring something with you/one
reinkommen - to come in
schlafen - to sleep
stehen - to stand
vergessen - to forget
waschen - to clean (in context of clean yourself or clean your car or do laundry)
wiederholen - to repeat
adjectives:
langsam - slow
leise - quiet / silent
typisch - typical
vorsichtig - careful
other words and expressions:
hinten - in the back / behind
links - left
rechts - right
sofort - immediately
später - later
vorne - in the front / ahead
Step-by-step explanation:
If not mistaken what the exercise asks, you need to fill in the articles of the German nouns and provide a translation to your language (I assume it's English?).
For figuring out the article of a noun, you only can memorize it / learn it by heart or look it up in a dictionary. The grammatical gender of nouns in German doesn't really makes much logical sense.