好意: kindness enabling help and affection kept private
Compare 好意で as kindness enabling an action with 好意を抱く as holding affection. Keep the helped action and private feeling separate from romance, confession, or reciprocal affection.
An action made possible by kindness
好意（こうい） means kindness or affection. 見知らぬ人の好意で重い荷物を運べた。 says that a stranger's kindness allowed the speaker to move heavy luggage.
好意で connects that kindness to what became possible. The sentence names the help and the enabled action; it does not make the stranger's kindness necessarily romantic.
A feeling held privately toward a colleague
彼女は同僚に密かな好意を抱いている。 says that she secretly has affectionate feelings for her colleague. 同僚に names the person toward whom the feeling is directed, and 好意を抱く describes holding it.
密かな indicates that the feeling is kept private. It does not establish that the colleague feels the same way or that a confession has already occurred.
Read the expression and its target
好意で and 好意を抱く illustrate kindness that enables help and affection toward someone. Their meanings need not be exclusive; the following action and the target of the feeling show the focus.
Receiving kindness does not confirm someone else's personal affection. Holding affection also differs from communicating it to the other person.
Does 彼女は同僚に密かな好意を抱いている。 show that her colleague has the same feelings?
Show the answer and why
No. It describes her privately held feelings toward the colleague. It does not report the colleague's feelings or the outcome of a confession.