If ROME is written as MORE, then DARE is written as

Let's analyze the letter shifting pattern in the word ROME to MORE:
$$\begin{array}{cccc}\text{R}& \text{O}& \text{M}& \text{E}\\ 1& 2& 3& 4\end{array}\to \begin{array}{cccc}\text{M}& \text{O}& \text{R}& \text{E}\\ 3& 2& 1& 4\end{array}$$

The pattern shows that the 1st and 3rd letters are interchanged, while the 2nd and 4th letters remain in their original positions.

Applying the exact same rule to DARE:

$$\begin{array}{cccc}\text{D}& \text{A}& \text{R}& \text{E}\\ 1& 2& 3& 4\end{array}\to \begin{array}{cccc}\text{R}& \text{A}& \text{D}& \text{E}\\ 3& 2& 1& 4\end{array}$$

Thus, DARE becomes RADE.