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The distributive law is a cornerstone of algebra that allows us to simplify expressions and solve equations efficiently. It states that for any three numbers, say, a, b, and c, the expression a(b + c) can be expanded to ab + ac. This is instrumental in breaking down complex expressions into simpler parts that are easier to deal with.

But the distributive law is not just for addition within the parentheses; it also applies to subtraction. For instance, if you have a(b - c), you can expand it to ab - ac. As evident in our original exercise, we don't have an addition or subtraction inside the parentheses. However, the principle still applies when distributing a multiplication over a single term within parentheses, effectively multiplying the outside number with the inside term.

Multiplying negative numbers can seem confusing at first, but it's based on a simple set of rules. When you multiply a negative number by a positive number, your answer is negative. On the other hand, when you multiply two negative numbers together, the negatives cancel out, and the result is positive.

This concept is pivotal when simplifying expressions such as our original exercise \( -4\left(-\frac{3}{4} y\right) \). The multiplication of the negative number -4 with another negative number -\(\frac{3}{4}\) leads to a positive result. It's the reason why our simplified expression is \(3y\) instead of staying negative or becoming more complex. Understanding how to multiply negative numbers is essential in algebra because it helps predict the sign of an answer and keeps the simplification process moving smoothly.

Linear operations in algebra refer to the basic arithmetic operations—addition, subtraction, multiplication, and division—that are performed in a straight-forward, 'line by line' manner. These operations are governed by the properties of real numbers and must follow the rules of arithmetic sequences.

In the context of algebraic expressions, linear operations help us maintain the integrity of equations while we simplify or solve them. An operation is linear if it satisfies two main properties: additivity (the ability to add two terms) and homogeneity of degree one (you can multiply by a scalar, and the term's degree doesn't change). The distributive law used in the exercise is a part of linear operations as it allows for the multiplication to be distributed over the term within the parenthesis, following these linear properties.