Is this a Boggle pad?
Python 3, 215 bytes



def f(w):b=product(*[set("".join(w))]*16);return any(all(any(all(x-y in[1,-1,4,-4]for x,y in zip(q,q[1:]))for q in product(*[[x for x in range(16)if k[x]==c]for c in a]))for a in w)for k in b)
from itertools import*


Try it online!

This is never going to finish, so I can't really debug it or prove it works. I will try to find constant optimizations / test with reduced test cases, but if you spot a reason it would definitely fail, I will take it down / fix it.