To simplify this expression, we need to distribute the coefficients inside the parentheses.

First, distribute the 2/7 to each term in the first set of parentheses:
2/7 4 = 8/7
2/7 2/3t = 4/7t
2/7 * -1 = -2/7

So, the first term becomes: 8/7 + 4/7t - 2/7

Now, distribute the -2/9 to each term in the second set of parentheses:
-2/9 6t = -12/9t = -4/3t
-2/9 2 = -4/9

So, the second term becomes: -4/3t - 4/9

Now, combine the terms from both sets of parentheses:
(8/7 + 4/7t - 2/7) - (4/3t + 4/9)

To subtract the second set of terms, you need to take the distributive negative sign into account:
8/7 + 4/7t - 2/7 - 4/3t - 4/9

Now, combine like terms:
4/7t - 4/3t + 8/7 - 2/7 - 4/9

Simplify the terms:
(4/7 - 4/3)t + (8/7 - 2/7 - 4/9)

Find a common denominator for each set of terms:
(12/21 - 28/21)t + (72/63 - 18/63 - 28/63)

Simplify:
(-16/21)t + (26/63)

So, the simplified expression is:
(-16/21)t + 26/63