The sentence in the Direct Speech is in Simple Present Tense. Therefore, the sentence in the Indirect Speech should be in Simple Past Tense.
Simple Present (Subject + V1 + Object) should be converted into Simple Past (Subject +V2 + Object).
"That" is used in place of Inverted Commas while transforming the sentence from Direct Speech to Indirect Speech.
For example:
He said, "I never go to the village." (Direct Speech)
He said that he never went to the village. (Indirect Speech)
The following things in the sentence should change when changed from Direct speech to Indirect Speech:
To convert the direct speech "I am determined..." into reported speech, the pronoun "I" changes to "she" (assuming the scientist is female, as implied by options), and the verb tense shifts back (present "am" to past "was").
Therefore, the correct answer is:
The correct sentence is: "The scientist confidently asserted that she was determined to publish her findings."