1. Write the ground-state electronic configuration of neutral Gd

Gadolinium has atomic number $64$. Its ground-state configuration is:

$\mathrm{Gd} = [Xe] \, 4f^7 5d^1 6s^2$

This is a well-known exceptional configuration due to the extra stability of half-filled $4f^7$.

2. Form $\mathrm{Gd}^{2+}$ by removing two electrons

When forming cations, electrons are removed first from the outermost shell (highest principal quantum number).

For Gd:

• $6s$ electrons are removed first.

So,

$\mathrm{Gd}^{2+} = [Xe] \, 4f^7 5d^1$

3. Count the number of $4f$ electrons

From

$\mathrm{Gd}^{2+} = [Xe] \, 4f^7 5d^1$

the number of electrons in the $4f$ subshell is

$7$

4. Final answer

The number of $4f$ electrons in $\mathrm{Gd}^{2+}$ is:

$\boxed{7}$