# Turing machines equivalence from reduction

Given the Halting problem, I’m trying to reduce it in order to show that $$\left\{ \left( \langle M_1\rangle,\langle M_2\rangle \right)| L(M_1)=L(M_2) \right\}$$, where $$M_1, M_2$$ are Turing machines, is undecidable. I’m having some trouble making sense of the answer given here. Why do we assume that $$M$$ will finish reading $$x$$ exactly after $$|x|$$ steps? And if $$M$$ doesn’t halt, why does $$M’$$ automatically accept the empty language, i.e return the constant zero function? Can it not except other strings, not just $$x$$?

I would appreciate it if someone could break down the general idea of that answer or maybe give me a few hints on how I can approach this problem differently.