Let's evaluate each expression step by step using the given values.

a) $y + x - |y|$, where $x = -1$ and $y = 6$:

1. Start by calculating $|y|$: $|y| = |6| = 6$

2. Substitute the values of $x$ and $y$ into the expression: $y + x - |y| = 6 + (-1) - 6$

3. Simplify the expression: $6 - 1 - 6 = -1$

So, the value of the expression is $\boxed{-1}$.

b) $\frac{y}{6}(y - x)$, where $x = -5$ and $y = -6$:

1. Substitute the values of $x$ and $y$ into the expression: $\frac{-6}{6}(-6 - (-5))$

2. Simplify the terms inside the parentheses: $-6 - (-5) = -6 + 5 = -1$

3. Now simplify the entire expression: $\frac{-6}{6} \times (-1) = -1 \times (-1) = 1$

So, the value of the expression is $\boxed{1}$.

Would you like further details on any of the steps? Here are some related questions to explore:

1. What is the general rule for evaluating absolute values in expressions?
2. How does the sign of numbers affect the outcome of arithmetic operations?
3. Can you explain how distribution works in expressions like $\frac{y}{6}(y - x)$?
4. What happens when we substitute negative values into an expression with absolute values?
5. What is the importance of parentheses in changing the outcome of expressions?

Tip: Always be mindful of the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) when simplifying expressions!