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To solve for the current \( I \) in the given circuit, we can apply **Kirchhoff's Voltage Law (KVL)**, which states that the sum of all voltages in a closed loop is zero. 

### Step-by-step solution:

1. **Label the circuit**: 
   - The circuit has two voltage sources: 3V on the left and 5V on the right.
   - There are two resistors: 4Ω (top) and 6Ω (bottom).
   - We assume the current \( I \) flows clockwise.

2. **Apply Kirchhoff's Voltage Law (KVL)**:
   In a clockwise direction around the loop, the KVL equation becomes:
   \[
   -3V + 4Ω \cdot I + 6Ω \cdot I + 5V = 0
   \]
   This comes from the fact that:
   - The 3V source is "negative" because it's opposite the current direction.
   - The 4Ω and 6Ω resistors produce voltage drops \( 4I \) and \( 6I \) respectively.
   - The 5V source is "positive" since it's in the direction of current flow.

3. **Simplify the equation**:
   \[
   -3 + 4I + 6I + 5 = 0
   \]
   Combine like terms:
   \[
   10I + 2 = 0
   \]

4. **Solve for \( I \)**:
   \[
   10I = -2
   \]
   \[
   I = -\frac{2}{10} = -0.2 \, \text{A}
   \]

### Conclusion:
The current \( I \) is \( -0.2 \, \text{A} \), meaning the actual current flows counterclockwise in the circuit (opposite to the assumed direction).

Would you like more details on this? Here are some related questions you might find helpful:

1. How does Kirchhoff's Voltage Law apply to more complex circuits?
2. What happens if the resistances in the circuit are not equal?
3. How would the current change if we change the voltage sources?
4. What is the significance of the negative sign in the current value?
5. How can we use Ohm's Law to verify the current calculation?

**Tip:** Always pay attention to the direction of current flow when solving circuits with multiple voltage sources, as it affects the sign of each term in the KVL equation.

This problem involves determining the current I in a circuit with two voltage sources and two resistors using Kirchhoff's Voltage Law. The equation ΣV = 0 is applied to find the current through the circuit.

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