If x = 6a + 8b + 9c, y = 2b - 3a - 6c and z = c - b + 3a, find :
`x - y +z`

Answer

To solve the expression \( x - y + z \) given the values of \( x \), \( y \), and \( z \), we will follow these steps:

### Step 1: Write down the expressions for \( x \), \( y \), and \( z \).
We have:
- \( x = 6a + 8b + 9c \)
- \( y = 2b - 3a - 6c \)
- \( z = c - b + 3a \)

### Step 2: Substitute the values of \( x \), \( y \), and \( z \) into the expression \( x - y + z \).
We can rewrite the expression as:
\[ x - y + z = (6a + 8b + 9c) - (2b - 3a - 6c) + (c - b + 3a) \]

### Step 3: Distribute the negative sign in front of \( y \).
This gives us:
\[ x - y + z = 6a + 8b + 9c - 2b + 3a + 6c + c - b + 3a \]

### Step 4: Combine like terms.
Now we will combine the terms for \( a \), \( b \), and \( c \):
- For \( a \):
\[ 6a + 3a + 3a = 12a \]
- For \( b \):
\[ 8b - 2b - b = 5b \]
- For \( c \):
\[ 9c + 6c + c = 16c \]

### Step 5: Write the final expression.
Putting it all together, we have:
\[ x - y + z = 12a + 5b + 16c \]

### Final Answer:
Thus, the final result is:
\[ \boxed{12a + 5b + 16c} \]