To simplify the expression \((14x + 6y) + (5x + 12y)\), we will combine the like terms.
First, combine the \(x\) terms:
- \(14x + 5x = 19x\)
Next, combine the \(y\) terms:
- \(6y + 12y = 18y\)
Putting it all together, the simplified expression is: \[ 19x + 18y \]
So, the coefficients for \(x\) and \(y\) are:
- \(19\) for \(x\)
- \(18\) for \(y\)
Therefore, the filled in blanks are: 19 for \(x\) and 18 for \(y\).