Proving "QUESTION" is NP-Complete by reduction from n-variable 3SAT
The reduction is straightforward, but what's likely tripping you up is that while 3CNF clauses seem to describe what's needed for a satisfying assignment, what they do more directly is describe what assignments won't work, and that's the insight you need to do the reduction.

Each clause will be converted into a QUESTION string of length $n$, where $n$ is the number of variables in the 3CNF formula.  Number the variables in the formula from 1 to $n$.  For each clause output a QUESTION string with a 0, 1 or ? in the position of the string corresponding to that variable's number.  Use 1 if the variable is negated in the clause, 0 if it is not negated and ? if it does not appear in the clause at all.

Example: the 3CNF formula has seven variables ($x_1$ ... $x_7$) and there is a clause ($x_1 \lor \lnot x_4 \lor x_7$) you would output the QUESTION string 0??1??0 .

Once all the clauses are converted to QUESTION strings, any $w$ string not covered by the QUESTION strings can be directly converted to a satisfying assignment for the 3CNF formula.  As in the QUESTION strings each position in $w$ corresponds to previously numbered variable.  But in $w$ each 0 represents a variable that should be negated in the satisfying assignment, and each 1 represents a variable that should not be negated.