Let's solve the given equation step by step:
The given equation is:
[tex]\[ 6y - 2(y + 1) = 3(y - 2) + 6 \][/tex]
First, let's expand and simplify both sides.
Start by distributing the terms inside the parentheses:
[tex]\[ 6y - 2(y + 1) - (3(y - 2) + 6) \][/tex]
Expand the terms:
[tex]\[ 6y - 2y - 2 - 3y + 6 - 6 \][/tex]
Now, combine like terms:
[tex]\[ (6y - 2y - 3y) - 2 + 6 - 6 \][/tex]
[tex]\[ (6y - 5y) - 2 \][/tex]
[tex]\[ y - 2 = 0 \][/tex]
Move the constant term to the other side of the equation to isolate [tex]\( y \)[/tex]:
[tex]\[ y = 2 \][/tex]
This means the solution to the equation is:
[tex]\[ y = 2 \][/tex]
Therefore, the correct answer from the given choices is:
[tex]\[ y = 2 \][/tex]
