The strongest base is :

Options

A. `CH_(3)-underset(CH_(3))underset(|)N-CH_(3)`
B.
C. `C_(6)H_(5)-underset(C_(6)H_(5))underset(|)N-C_(6)H_(5)`
D. `CH_(3)-NH-CH_(3)`

Explanation

To determine the strongest base among the given options, we need to analyze the structures and the electron-donating effects of the substituents present in each compound. Here's a step-by-step breakdown of the solution:

### Step 1: Understand Basicity
Basicity refers to the ability of a compound to accept protons (H⁺ ions). The stronger the base, the more readily it can accept a proton. Basicity is influenced by the electron density around the basic site (usually a nitrogen atom in amines).

### Step 2: Analyze the Given Options
Assuming we have four options (A, B, C, D), we need to evaluate each based on their substituents and the electron-donating effects.

### Step 3: Evaluate Each Option
1. **Option A**: Contains a nitrogen atom with a double bond (NH) and possible resonance structures. The presence of resonance can stabilize the base, but it can also delocalize the electron density, which may reduce basicity.

2. **Option B**: Contains a nitrogen atom with two methyl groups. Methyl groups are electron-donating through the +I effect, which increases electron density on the nitrogen, making it a stronger base.

3. **Option C**: Contains a nitrogen atom with three benzene rings. The benzene rings can withdraw electron density due to resonance, making the nitrogen less basic.

4. **Option D**: Similar to option C, but with only two methyl groups. While methyl groups do donate electrons, the presence of multiple benzene rings will still dominate the electron-withdrawing effect.

### Step 4: Compare Options A and B
- In **Option A**, the NH group is involved in resonance, which can stabilize the base but also reduce its ability to accept protons.
- In **Option B**, the nitrogen is surrounded by two methyl groups that strongly donate electrons, enhancing its basicity.

### Step 5: Conclusion
Based on the analysis, **Option B** is the strongest base because it has two methyl groups that significantly increase the electron density on the nitrogen, allowing it to accept protons more readily than the other options.

### Final Answer
**The strongest base is Option B.**

---