'Manxome' is a word invented by Lewis Carroll which he used to describe the monstrous Jabberwock in his poem
Jabberwocky, but it is one for which he never gave a definition.
He took his vorpal sword in hand:
Long time the manxome foe he sought --
So rested he by the Tumtum tree,
And stood awhile in thought.
As such, we as readers have to define the word and choose a meaning for ourselves.
According to Dr Bill Long, the word is a portmanteau of the words 'manly' and 'buxom' and means 'fearsome' (See related link)
However, there is no evidence that this was Carroll's intention when he invented the word and as it does not follow the usual rules of portmanteau, this seems unlikely to be accurate.
In other portmanteau words, the new word carries the combined meaning of the words of which it is composed, for example 'mimsy' means 'miserable' and 'flimsy' and those are the words which comprise it. But, as the old uses of the word 'buxom' were 'vivacious' and 'compliant', it does not seem possible that when combined with the word 'manly' this would create the meaning 'fearsome'.
It is more likely that 'manxome' is not a portmanteau of 'manly' and 'buxom' at all and is one of the words in
Jabberwocky which lacks a definitive meaning.