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When it rains and the soil gets moist, weeds become easier to pull.
Literal
Rain [subject-が] fall-and soil [on-に] moisture [subject-が] exist [when-と], weeds [topic-は] easy-to-pull become.
A gardening tip. 湿り気 ('moisture, dampness') is the noun form of 湿る ('become damp') + the suffix 気 (an abstracted 'quality' marker similar to ~性). Found in words like 色気 ('sexiness'), 勇気 ('courage'), 湿り気 ('dampness'). 取りやすい ('easy to take/pull') uses the ~やすい auxiliary attached to 取る ('take, pull, remove'). In gardening context, 草を取る means 'to pull weeds.' The ~と conditional expresses the automatic/natural connection: 'when it rains and the soil is moist, [then] weeds become easier.'