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The distributive property is a very handy tool in algebra. It allows you to simplify expressions by eliminating parentheses. The basic idea is to multiply each term inside the parentheses by the number outside. In our example, we have two instances where we need to apply the distributive property:

- For the expression \(-7.5(2y + 4)\), distribute the \(-7.5\) to both \(2y\) and \(4\). This gives us \(-7.5 \cdot 2y\) and \(-7.5 \cdot 4\).

- Similarly, for the expression \(-2.9(3y - 6)\), distribute the \(-2.9\) to both \(-3y\) and \(-6\). This results in \(-2.9 \cdot 3y\) and \(+2.9 \cdot 6\) (remember the sign change because of the subtraction).

This step simplifies the problem significantly and prepares the numbers and variables for easier multiplication and combination.

After using the distributive property, the next step is to perform the actual multiplications. Let's look at each multiplication separately:

- \(-7.5 \cdot 2y = -15y\)

- \(-7.5 \cdot 4 = -30\)

- \(-2.9 \cdot 3y = -8.7y\)

- \(2.9 \cdot 6 = 17.4\)

At this stage, it's important to be careful with the signs (positive and negative) and ensure each multiplication is performed correctly. Multiplying coefficients involves focusing on the number parts of each term and then multiplying those numbers directly. The variable part (like \(y\)) is simply carried along in the multiplication.

Finally, we need to combine like terms to completely simplify the expression. Like terms have the same variable part, so in our example, we'll combine the terms involving \(\text{y}\) together and the constant terms (numbers without variables) together:

- Combine \(-15y\) and \(-8.7y\). This gives \(-15y - 8.7y = -23.7y\).

- Next, combine the constant terms \(-30\) and \(17.4\). This results in \(-30 + 17.4 = -12.6\).

By combining like terms, you're consolidating the expression to its simplest form. The final simplified expression in our example is \(-23.7y - 12.6\). This makes it easier to read and understand, ensuring you have a clear solution.