Consider the compute decision problem: Does Turing machine M compute u on input w?

A notation for the yes answer is:

q0 ^w |--*M q f ^u

Meaning: If M starts in state q₀ with its read-write head positioned on the first character in w, then after some sequence of moves, M is arrive in a final state q_f with some string u on the tape.

For a no answer, machine M can make no sequence of moves from q₀w to q_fu.

Show that there is no Turing machine M_C that decides the compute problem. That is, there is no machine M_C whose behavior is:

M_C(M, w,u) = { yes q₀w |--* M q _f u

no otherwise

(Hint: Assume M_C exists and use it to construct a Turing machine that decides the halting problem. Use a machine M' that enumerates all of the strings u * .)

Explain plz. I want to learn