Analysis of the Circuit:
- The circuit consists of a 6 ohm resistor and an unknown resistor, represented by the symbol "R".
- The power dissipated as heat in the 6 ohm resistor is given as 6 W.

Calculating the Power Dissipated:
- The power dissipated in a resistor can be calculated using the formula: P = I^2 * R, where P is the power, I is the current flowing through the resistor, and R is the resistance.
- In this case, the power dissipated in the 6 ohm resistor is given as 6 W. Let's denote the current flowing through the 6 ohm resistor as I_1.
- Therefore, we have: 6 = I_1^2 * 6.

Calculating the Current:
- We can solve the equation for I_1 by rearranging the formula: I_1 = sqrt(6/6) = 1 A.
- This means that the current flowing through the 6 ohm resistor is 1 A.

Applying Kirchhoff's Voltage Law:
- According to Kirchhoff's Voltage Law, the sum of voltage drops in a closed loop is equal to the sum of voltage rises.
- In this circuit, the voltage drop across the 6 ohm resistor is 6 V (since P = VI, and we know that P = 6 W and I = 1 A).
- Let's denote the voltage drop across the unknown resistor R as V_R.

Calculating the Voltage Drop:
- Applying Kirchhoff's Voltage Law, we have: V_R + 6 = 0.
- Solving the equation, we find that V_R = -6 V.

Calculating the Resistance:
- The voltage drop across a resistor can be calculated using the formula: V = I * R, where V is the voltage drop, I is the current flowing through the resistor, and R is the resistance.
- In this case, we have: -6 = 1 * R.
- Therefore, the resistance R is equal to -6 ohms.

Conclusion:
- The value of the resistance R in the circuit is -6 ohms.