Can someone explain this in more detail? I don't understand why you should multiply by -3

We need to find the value for 18y-21x

by multiplying the original with -3 will give us the value for Qt A, which is less than -12

\(7x – 6y > 4\)

Quantity A	Quantity B
\(18y – 21x\)	\(-12 \)

The above posters are using the following property: a - b = (-1)(b - a)

The given information tells us that: 7x – 6y > 4
If we multiply both sides of the inequality by 3, we get the equivalent inequality: 21x – 18y > 12

The left side of the inequality, 21x - 18y, looks a lot like Quantity A, except the terms are reversed.
So we can apply the above property and take 21x – 18y > 12 and multiply both sides of the inequality by -1 to get -21x + 18y < -12 (Aside: I multiplied both sides of an inequality by a NEGATIVE value, I had to REVERSE the direction of the inequality symbol)

We can rearrange -21x + 18y < -12 as follows: 18y - 21x < -12

At this point it's clear that Quantity B is greater

Before solving the question, remember that if we multiply the two sides of an inequality sign, always flip the sign. Here we see that simply multiplying by 3 will bring the equation to same value. After that multiply by -1 and flip signs. We get -> 18y - 21x < -12
Hence Qb>Qa