Reduction from Clique to IS degree at most 4
As you stated, this is not a correct reduction, because you would need to solve Clique for any graph (or prove that Clique with graphs of degree at most 4 is $NP$-complete).
Actually, the question 8.6.b stands true if the graph have degree at most 3. I think the intention of the author for solving this exercice is to use the remark stated at the beginning of the exercice (which you cropped): &quot;$\textsf{3SAT}$ remains $\textsf{NP}$-complete even when restricted to formulas in which each litteral appears at most twice&quot;.
You should then make a reduction from $\textsf{3SAT-2LITmax}$ (a convenient name I came up for the problem I just described), using the same kind of reduction to prove $\textsf{NP}$-hardness of $\textsf{IS}$ from $\textsf{3SAT}$.