Step 1: Understand the meaning of the underlined word.
"Decollate" means to behead, which makes no sense in this context. The sentence needs a word that means to investigate or examine.
Step 2: Evaluate the options.
delve: Followed by "into," it means to research or make a detailed inquiry into something. "Delve into the matter" is a standard and appropriate phrase.
deduce: To arrive at a conclusion by reasoning. You deduce a fact, you don't deduce into a matter.
deflect: To cause something to change direction. You deflect criticism or a question, not a matter.
Step 3: Choose the best fit.
"Delve into" is the correct phrasal verb to express the idea of investigating the matter deeply.