One day like this, encountered myself twice (8)
I believe the answer is:
sometime
'one day' is the definition.
(I've seen this before)
'like this encountered myself twice' is the wordplay.
'like this' becomes 'so' ('like so').
'encountered' becomes 'met' ('meet' can be a synonym of 'encounter').
'myself' becomes 'I'.
'twice' becomes 'me' (I can't justify this - if you can you should give a lot more credence to this answer).
'so'+'met'+'i'+'me'='SOMETIME'
Can you help me to learn more?
(Other definitions for sometime that I've seen before include "Formerly" , "One day" , "At an unknown moment" , "Former; occasional (US)" , "In the future, we don't know when" .)