It's All Latin (the phrase is a hint for the Latin root)
The Latin term found in gradual, graduate, downgrade
grade
The Greek term found in melanin, melancholy, and melanoma
mela
radi-ray
radiation, radical, radius
ob
The old barn was infested with vermin like rats and mice, scurrying around in search of food.
worm
The Latin term found in vice versa, vice president, viceroy
vice
The Greek term found in atomic, subatomic, atomize
atom
vect-carry
Convection, Vector, Invective
finger-Latin-
digit
Over time, the fallen tree began to lignify, turning into solid wood as it decomposed.
wood
The Latin term found in folio, portfolio, foliage
foli
The Greek term found in hemisphere, hemialgia
hemi
narcolepsy, narcotic
form-Greek-
plasm
The Earth is divided into hemispheres: the northern hemisphere and the southern hemisphere
half
The Latin term for many
multi
The Greek term for lung
pneumo
ign-fire
ignite, reignite, ignition
carry-Latin-
vect
The circles on the Venn diagram osculate where they overlap.
mouth
The Latin term for soft
moll
The Greek term for egg
oo
orb-circle
orbit, exorbitant, orbital
tear-Latin
lachry
The gymnasium was empty during the summer when students were not in school.
naked