To solve the expression \(-( \frac{3}{7} + \frac{3}{8} ) - ( -\frac{3}{8} + \frac{4}{7} )\), we need to follow the order of operations (PEMDAS/BODMAS). Let's break it down step by step:

1. Simplify inside the parentheses:
\[
\frac{3}{7} + \frac{3}{8}
\]
To add these fractions, we need a common denominator. The least common multiple of 7 and 8 is 56. Convert each fraction:
\[
\frac{3}{7} = \frac{3 \times 8}{7 \times 8} = \frac{24}{56}
\]
\[
\frac{3}{8} = \frac{3 \times 7}{8 \times 7} = \frac{21}{56}
\]
Now add them:
\[
\frac{24}{56} + \frac{21}{56} = \frac{45}{56}
\]

2. Simplify the second part inside the parentheses:
\[
-\frac{3}{8} + \frac{4}{7}
\]
Again, find a common denominator, which is 56:
\[
-\frac{3}{8} = -\frac{3 \times 7}{8 \times 7} = -\frac{21}{56}
\]
\[
\frac{4}{7} = \frac{4 \times 8}{7 \times 8} = \frac{32}{56}
\]
Now add them:
\[
-\frac{21}{56} + \frac{32}{56} = \frac{11}{56}
\]

3. Substitute these results back into the original expression:
\[
-\left( \frac{45}{56} \right) - \left( \frac{11}{56} \right)
\]

4. Simplify the expression:
\[
-\frac{45}{56} - \frac{11}{56} = -\left( \frac{45}{56} + \frac{11}{56} \right) = -\frac{56}{56} = -1
\]

So, the value of the expression \(-( \frac{3}{7} + \frac{3}{8} ) - ( -\frac{3}{8} + \frac{4}{7} )\) is \(-1\).