"confusticate and bebother those dwarves!"
-- J.R.R. Tolkien, The Hobbit
Confusticate means to make more confusing, or to confuse and confound someone or something. It is a made-up word, but we don't actually know who invented it, so the exact definition is a little up in the air. For all practical purposes, it is defined by that one sentence in The Hobbit, as it would have been the smallest of historical footnotes if Tolkien had not used it.
The earliest source for confusticate that I can find is in 1866, when W. S. Gilbert (of the famous Gilbert & Sullivan) used it in his mini-musical Ruy Blas, which was published in Warne's Christmas Annual:
When first I went a-governing,
A-governing did go,
I thought to have my own way --
That none, should say me "No!" --
But ere I had been at it long,
I found it wasn't so-o-o.
I had to come and go,
Receive with pomp and show
From nations, deputations,
Which confusticate one so!
I would not be at all surprised if it was Mr. Gilbert who coined this word, trying to find a word that was both appropriately comical and that fit the meter properly. Both these factors would explain the need to elongate the otherwise sufficient word 'confuse'.
Ever since the time of Romans, those of us that speak Romance languages have had fun playing with Latin suffixes and prefixes, creating new words out of whole cloth or adding on to the words we use every day. We created conundrum in 1596, hocus-pocus in 1624, millennium in 1638, transmogrify in the mid-1600s, floccinaucinihilipilification in 1741, and the famously confused sociology in 1843. In the mid-1800s a lot of these words were created, including calibrate, discombobulate, obfusticated, absquatulate, bloviate, and others even more obscure. Amongst these words appeared confusticate. It was quickly forgotten -- until Tolkien used it one of the most famous fantasy books of all time. It has since become a little bit popular among those who like odd words, although it's still an oddity by anyone's standards.
In so far as we can deconstruct it, confusticate breaks down thusly: confus- (from the English confuse, coming in turn from the Latin confusus) -tic- (apparently because it just sounds better with a -tic- in the middle), and -ate (which after almost 2000 years has lost any specific meaning, and especially so in this case).