Distance I ran into outskirts of Rome at end of last month (9)

'distance' is the definition.
Although both the answer and definition are singular nouns, I can't see how one could define the other.

'i ran into outskirts of rome at end of last month' is the wordplay.
'ran into' becomes 'met'.
'outskirts of' says to hollow out the word (remove centre letters).
'at end of' is a charade indicator (letters next to each other).
'last month' becomes 'dec'.
'rome' with its centre removed is 're'.
'i'+'met'+'re'='imetre'
'imetre' after 'dec' is 'DECIMETRE'.

Can you help me to learn more?