How many ATP molecules are produced thorough ETS, out of 38...

During the complete oxidation of one glucose molecule, a total of $38$ ATP molecules are produced.

Substrate-level phosphorylation (SLP) directly yields ATP without the involvement of the Electron Transport System (ETS). The ATP produced via SLP is:
Glycolysis: $2$ ATP
Krebs cycle: $2$ ATP (one per turn, two turns per glucose)
Total ATP from SLP = $4$ ATP.

The remaining ATP molecules are generated through oxidative phosphorylation via the ETS from reduced coenzymes (NADH and FADH_2$). \\ Total ATP from ETS = Total ATP$-$ATP from SLP \\ Total ATP from ETS = 38 - 4 = 34$ ATP. \\ \\ Alternatively, calculating from reduced coenzymes: \\ Glycolysis: $2$ NADH \rightarrow 6$ATP \\ Link reaction: 2$ NADH $\rightarrow 6$ ATP \\ Krebs cycle: $6$ NADH $\rightarrow 18$ ATP and $2$ FADH_2\rightarrow 4$ATP<br>Total ATP from ETS = 6 + 6 + 18 + 4 = 34$ ATP.

Answer: $34$