The most common and most likely answer to this crossword clue is the 6 letter word SLOPES
I've seen this crossword clue in Financial Times
S
L
O
P
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Buddy explains!
The straight part
We know that "hillsides" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case hillsides = slopes.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does SLOPES mean?
SLOPES noun- An area of ground that tends evenly upward or downward.
- The degree to which a surface tends upward or downward.
- The ratio of the vertical and horizontal distances between two points on a line; zero if the line is horizontal, undefined if it is vertical.
- The slope of the line tangent to a curve at a given point.
- The angle a roof surface makes with the horizontal, expressed as a ratio of the units of vertical rise to the units of horizontal length (sometimes referred to as run).
- A person of Chinese or other East Asian descent.
- To tend steadily upward or downward.
- To form with a slope; to give an oblique or slanting direction to; to incline or slant.
- (usually followed by a preposition) To try to move surreptitiously.
- To hold a rifle at a slope with forearm perpendicular to the body in front holding the butt, the rifle resting on the shoulder.