ay-3y-4a+12

To simplify the expression \( ay - 3y - 4a + 12 \), you can rearrange and group the similar terms:

1. Group the \( a \) terms and the \( y \) terms:

   • Group \( ay \) and \( -3y \)
   • Group \( -4a \) and \( +12 \)

2. Rewrite the expression: \[ ay - 3y - 4a + 12 = (ay - 3y) + (-4a + 12) \]

3. From here, you can factor out common terms: \[ = y(a - 3) - 4(a - 3) \]

4. Notice that both terms share a common factor of \( (a - 3) \): \[ = (a - 3)(y - 4) \]

So, the simplified expression is: \[ (a - 3)(y - 4) \]