1. Count total valence electrons

For $NO_2^-$:

• Nitrogen contributes $5$ valence electrons.
• Two oxygen atoms contribute $2 \times 6 = 12$ valence electrons.
• The negative charge adds $1$ extra electron.

So total valence electrons are: $5 + 12 + 1 = 18$

2. Draw the Lewis structure

The nitrite ion, $NO_2^-$, has nitrogen as the central atom. A valid Lewis structure has:

• one $N=O$ double bond,
• one $N-O^-$ single bond,
• one lone pair on nitrogen.

There are two equivalent resonance structures, but the total number of non-bonded electrons remains the same in either one.

3. Count bonding electrons

In one resonance structure:

• one double bond has $4$ bonding electrons,
• one single bond has $2$ bonding electrons.

Total bonding electrons: $4 + 2 = 6$

4. Find non-bonded electrons

Non-bonded electrons are: $18 - 6 = 12$

5. Check by direct lone-pair counting

• Double-bonded oxygen has $2$ lone pairs $= 4$ electrons
• Single-bonded oxygen has $3$ lone pairs $= 6$ electrons
• Nitrogen has $1$ lone pair $= 2$ electrons

Total non-bonded electrons: $4 + 6 + 2 = 12$

Thus, the total number of non-bonded electrons in $NO_2^-$ is: $\boxed{12}$