Let's break down the expressions \( A \) and \( B \) step by step.

### Expression \( A \):
\[ A = \frac{1}{2} - \frac{3}{4} + \frac{5}{6} - \frac{7}{12} \]

First, let's find a common denominator for all the fractions. The denominators are 2, 4, 6, and 12. The least common multiple (LCM) of these numbers is 12.

Convert each fraction to have a denominator of 12:
\[ \frac{1}{2} = \frac{6}{12} \]
\[ \frac{3}{4} = \frac{9}{12} \]
\[ \frac{5}{6} = \frac{10}{12} \]
\[ \frac{7}{12} = \frac{7}{12} \]

Now substitute these back into the expression:
\[ A = \frac{6}{12} - \frac{9}{12} + \frac{10}{12} - \frac{7}{12} \]

Combine the fractions:
\[ A = \frac{6 - 9 + 10 - 7}{12} \]
\[ A = \frac{0}{12} \]
\[ A = 0 \]

### Expression \( B \):
\[ B = -3 - \frac{2}{3} + \frac{3}{5} \left( -\frac{10}{9} - \frac{25}{3} \right) - \frac{5}{6} \]

First, simplify the expression inside the parentheses:
\[ -\frac{10}{9} - \frac{25}{3} \]

Convert \(\frac{25}{3}\) to have a denominator of 9:
\[ \frac{25}{3} = \frac{75}{9} \]

Now combine the fractions:
\[ -\frac{10}{9} - \frac{75}{9} = -\frac{85}{9} \]

Now multiply this result by \(\frac{3}{5}\):
\[ \frac{3}{5} \left( -\frac{85}{9} \right) = -\frac{255}{45} \]

Simplify \(\frac{255}{45}\):
\[ \frac{255}{45} = \frac{17}{3} \]

Now substitute back into the expression for \( B \):
\[ B = -3 - \frac{2}{3} - \frac{17}{3} - \frac{5}{6} \]

Combine the fractions with a common denominator of 6:
\[ -3 = -\frac{18}{6} \]
\[ -\frac{2}{3} = -\frac{4}{6} \]
\[ -\frac{17}{3} = -\frac{34}{6} \]
\[ -\frac{5}{6} = -\frac{5}{6} \]

Now combine all the fractions:
\[ B = -\frac{18}{6} - \frac{4}{6} - \frac{34}{6} - \frac{5}{6} \]
\[ B = -\frac{18 + 4 + 34 + 5}{6} \]
\[ B = -\frac{61}{6} \]

So, the final values are:
\[ A = 0 \]
\[ B = -\frac{61}{6} \]