Kraft Macmillan inequality explanation
I think it's just in the first inequality (the Kraft inequality): you sum over all the symbols $1/2^{\text{length of encoding}}$. There are 3 symbols of length $3$ bits and $d$ symbols of length $8$ bits, so that's how you get the first inequality. (Also, does your question have a typo? $a_4,a_5,\dots,a_{d+3}$ rather than $\dots,a_{d+1}$.) The $5/8$ comes from simplifying the inequality: you get $3/8 + d/256 \leq 1$, which is equivalent to $d/256 \leq 5/8$.