A biodegradable polyamide can be made from:

We recall that a polyamide is obtained by repeated formation of the amide linkage, which has the characteristic $$-\,\mathrm{CO\,NH}-$$ group. Biodegradability is favoured when the backbone contains short peptide-like segments that hydrolyse easily; this usually happens when at least one monomer is an α-amino acid, that is, a molecule possessing both $$\mathrm{-NH_2}$$ and $$\mathrm{-COOH}$$ on the same carbon. Hence we must look for a pair of monomers that together furnish many amide bonds and at least one naturally peptide-type centre.

Let us inspect each option one by one.

Option A (Glycine and isoprene)
Glycine has the desired $$\mathrm{-NH_2}$$ and $$\mathrm{-COOH}$$ groups, but isoprene $$\big(\mathrm{CH_2=C(CH_3)CH=CH_2}\big)$$ contains only carbon-carbon double bonds and no carboxyl or amino group. Therefore no amide bond can be produced between the two; polymerisation would proceed, if at all, by a radical mechanism on the isoprene alone, not by condensation. So a polyamide cannot form.

Option B (Hexamethylene diamine and adipic acid)
These two compounds do indeed undergo the condensation reaction $$\mathrm{H_2N\,(CH_2)_6\,NH_2 + HOOC\,(CH_2)_4\,COOH} \;\longrightarrow\; \Big[-\mathrm{NH\,(CH_2)_6\,NHCO\,(CH_2)_4\,CO}-\Big]_n$$ which is well known as Nylon-6,6. However, Nylon-6,6 contains long aliphatic segments $$\mathrm{(CH_2)_6}$$ and $$\mathrm{(CH_2)_4}$$ on either side of each amide linkage; those hydrophobic chains hinder enzymatic attack, so the material is not classified as biodegradable.

Option C (Glycine and aminocaproic acid)
Write the structures: $$\text{Glycine: } \mathrm{H_2NCH_2COOH}$$ Aminocaproic acid: $$\mathrm{H_2N\,(CH_2)_5\,COOH}$$ Both molecules possess the pair $$\mathrm{-NH_2}$$ and $$\mathrm{-COOH}$$, so each can act simultaneously as an acid and as a base in the condensation. When heated, they combine with elimination of water: $$\mathrm{H_2NCH_2COOH + H_2N\,(CH_2)_5\,COOH} \;\longrightarrow\; \Big[-\mathrm{NHCH_2CO\,NH\,(CH_2)_5\,CO}-\Big]_n + n\,\mathrm{H_2O}$$ The repeat unit contains two successive peptide bonds resembling those in natural proteins: $$\Big[-\,\mathrm{NH\,CH_2\,CO\,NH\,(CH_2)_5\,CO}-\Big]_n$$ Because the amide linkages lie next to relatively short segments (one methylene on one side and five on the other), hydrolytic and enzymatic cleavage occurs readily, making the polymer biodegradable. Indeed, this particular copolymer is historically named “Nylon-2-Nylon-6” where the numerals refer to the carbon counts in the two amino acids. Therefore, this combination satisfies the requirement.

Option D (Styrene and caproic acid)
Styrene $$\big(\mathrm{C_6H_5CH=CH_2}\big)$$ lacks both $$\mathrm{-NH_2}$$ and $$\mathrm{-COOH}$$ groups, so no amide bond can form with caproic acid $$\big(\mathrm{HOOC\,(CH_2)_5\,CH_3}\big)$$. Polymerising styrene gives polystyrene, which is not a polyamide, and mixing it with a carboxylic acid does not change that fact.

Only Option C deploys two amino acids whose condensation produces a peptide-like, hence biodegradable, polyamide chain. The other pairs either cannot form an amide polymer at all or yield a well-known non-biodegradable nylon.

Hence, the correct answer is Option C.