Ok, so what we want to do here is first remove the repeating decimal.
x=2.16 repeating
10x=21.6 repeating
100x=216.6 repeating
Subtract 10x=21.6 repeating from 100x=216.6 repeating. This will get rid of the repeating numbers.
100x=216.6 repeating
-10x=21.6 repeating
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90x=195
Divide both sides by 90.
x=195/90
Now you can simplify that into 13/6.