Up to one's knuckles; with the whole hand in; so as to be deeply implicated or involved.
The Century Dictionary (Public Domain)
Use "knuckle-deep" in a sentence
"He's the epitome of the Hollywood hyphenate, a writer-producer-editor-director who keeps his fingers knuckle-deep in the production pie long after a series launches."
"Free Companions, be knuckle-deep in the English budgets — “And, like jovial hunters,” replied the knight,"
"Veronique's hands stilled, knuckle-deep in foamy goo."