Your strings can start with any number of 0's or 10's. These don't contain any 110. So we start with $(0 | 10)^*$.

The remainder of the input mustn't contain any zeroes: If the remainder starts with no 1 or one 1, then that cannot be followed by a zero, because 0 or 10 would be part of $(0 | 10)^*$. If there are $n \ge 2$ 1's, that cannot be followed by a 0 because then we would have $1^{n-2} 110$ which is by definition not part of the language. So the rest of the input is $1^*$, and the regular expression is $(0 | 10)^* 1^*$.

Your strings can start with any number of 0's or 10's. These don't contain any 110. So we start with $(0 | 10)^*$.

The remainder of the input mustn't contain any zeroes: If the remainder starts with no 1 or one 1, then that cannot be followed by a zero, because 0 or 10 would be part of $(0 | 10)^*$. If there are $n \ge 2$ 1's, that cannot be followed by a 0 because then we would have $1^{n-2} 110$ which is by definition not part of the language. So the rest of the input is $1^*$, and the regular expression is $(0 | 10)^* 1^*$.

OP's answer is also correct, but this grammar is simpler, and any string can be parsed in one way only.