Introduction
In order to determine if 8.6 * 10^-19 coulombs of charge can be given to a conductor, we need to consider the concept of charge and the properties of conductors.

Charge and Conductors
Charge is a fundamental property of matter that can be positive or negative. In a conductor, charges are free to move due to the presence of loosely bound electrons. When a conductor is brought in contact with a charged object, the charges redistribute themselves on the surface of the conductor until equilibrium is reached. This redistribution occurs in a way that the electric field inside the conductor is zero.

Determining the Capacity of a Conductor
The capacity of a conductor to hold charge is determined by its capacitance, which depends on various factors such as the size, shape, and material of the conductor. The capacitance is given by the equation C = Q/V, where C is the capacitance, Q is the charge, and V is the potential difference.

Calculating the Charge
Given that the charge Q is 8.6 * 10^-19 coulombs, we need to determine if this charge can be accommodated by the conductor. To do this, we need to know the capacitance of the conductor.

Insufficient Information
Unfortunately, the question does not provide any information about the capacitance of the conductor. Without this information, we cannot determine if the given charge can be accommodated by the conductor. The capacitance could vary depending on the size, shape, and material of the conductor.

Conclusion
In conclusion, without the information about the capacitance of the conductor, we cannot determine if 8.6 * 10^-19 coulombs of charge can be given to the conductor. The capacitance of the conductor plays a crucial role in determining its capacity to hold charge. Therefore, additional information is required to answer the question accurately.