To simplify the expression, first distribute the negative sign inside the brackets:

2 1/6y - 7x + 1 3/4y + 2 1/5x

Next, combine like terms:

-7x + 2 1/6y + 1 3/4y + 2 1/5x

Now, add or subtract the coefficients of like terms:

-7x + 2 1/6y + 1 3/4y + 2 1/5x
= -7x + 3 7/12y + 2 1/5x

Therefore, the simplified expression is -7x + 3 7/12y + 2 1/5x.