Final answer:
The identity or property used at the beginning is the Distributive Property, which involves multiplying each term inside the parentheses by the factor outside. This simplifies the equation, allowing for the combination of like terms and isolation of the variable 'x'.
Step-by-step explanation:
The identity or property used during the first step when solving the equation 2/3 - 8x = 1/6(4x - 1) is the Distributive Property. The Distributive Property allows you to multiply each term inside the parentheses by the factor outside of the parentheses. This results in the equation becoming 2/3 - 8x = 4x/6 - 1/6.
To further solve the problem, you would combine like terms and isolate the variable. This could involve moving all terms containing x to one side and the constant terms to the other, followed by combining and reducing fractions if possible. For example, combining like terms might simplify the equation to 12x/6 - 1/6 on one side. Then, you would typically multiply each term by the least common denominator to clear the fractions and solve for x. Finally, possible further steps could include dividing by the coefficient of x to find its value.