The cat has not gained a single letter
Write CAT on three scraps of paper. Slide the C to the middle: ACT. Nothing has been added or thrown away, yet the animal has turned into something you can do.
An anagram rearranges all the letters of a word or phrase to make another word or phrase. The letters move; their counts stay the same. That is the idea in Merriam-Webster’s definition.
LISTEN → SILENT is a pleasing example. It sounds like someone has hidden an instruction inside the word. In fact, the puzzle only needs the matching letters; the meanings do not have to be related.
Your letters are a tiny budget
A tempting answer can look right and still spend a letter you do not have. CAT → CATS fails because the S came from nowhere. BOOK → BOO fails because the K has disappeared.
Repeated letters are where this gets sneaky. BOOK gives you two Os, not one. Write the letters in a row and cross off each one as you use it. A valid answer uses every original letter, including repeats.
Sorting both words alphabetically is another quick check: LISTEN and SILENT both become EILNST. Their letter budgets match exactly.
One stone, two surprises
Take STONE. Can you turn it into something a musician might play? Keep all five letters.
Show one answer
TONES. You can also rearrange STONE into NOTES. Both use S, T, O, N and E exactly once.
If you get stuck, try moving the vowels first. Or look for a familiar ending. Neither trick guarantees an answer, but changing the arrangement can help you stop reading the original word automatically.
Same letters, different trick
Anagrams shuffle letters. Palindromes keep the order and read the same backwards. That distinction is handy: CAT and ACT are an anagram pair, but neither word is a palindrome.
For a little challenge, rearrange TEA into a word meaning “consume food”. Then see if there is another real word hiding in the same three letters.
Check your words
EAT fits the clue. ATE uses the same letters too, with the action moved into the past.