The most common and most likely answer to this crossword clue is the 12 letter word AMBIDEXTROUS
I've seen this crossword clue in The Times
A
M
B
I
D
E
X
T
R
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S
Buddy explains!
The straight part
We know that "using both right and left" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case using both right and left = ambidextrous.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 AMBIDEXTROUS mean?
AMBIDEXTROUS adjective- Having equal ability in both hands; in particular, able to write equally well with both hands.
- Equally usable by left-handed and right-handed people (as a tool or instrument).
- Practising or siding with both parties.
- Of a person, bisexual.
- Exceptionally skillful; adept in more than one medium, genre, style, etc.