Subtract (3b-2c) - (2b + 6c) - (b + c)

First, let's distribute the negative sign in front of each term inside the parentheses:

-(3b-2c) = -3b + 2c
-(2b + 6c) = -2b - 6c
-(b + c) = -b - c

Now we can rewrite the expression as:

(-3b + 2c) - (2b + 6c) - (b + c)

Next, let's combine like terms:

-3b - 2b - b + 2c - 6c - c

Simplifying further:

-6b - 5c