An isotropic material — one with the same properties in every direction, which covers nearly every metal you will meet — does not get to choose its three elastic constants independently. They are locked together: $E = 2G(1 + \nu)$, read E equals two G, times one plus nu. $E$ is Young's modulus, $G$ the shear modulus, $\nu$ Poisson's ratio, all three for the same material. Know any two and the third is arithmetic, never a second test.

Sanity-check every answer against the shape of the identity. With $\nu$ near 0.3 the bracket is near 1.3, so $E$ lands near $2.6\,G$: the shear modulus of a metal always comes out around two-fifths of its Young's modulus. Steel at 200 GPa carries $G$ near 77; aluminium at 70 carries $G$ near 26. If your $G$ ever arrives larger than your $E$, you have multiplied where the identity divides.

The mistake this lesson exists to prevent is smaller and much quieter: dropping the $(1 + \nu)$ bracket and writing $G = E/2$. It is not wildly wrong, which is precisely why it survives a whole calculation — it overstates the shear modulus by a quarter to a third, and nothing about the answer looks strange on the way past.