Add:
`3a - 4b + 4c, 2a + 3b - 8c, a - 6b + c`

Answer

To add the algebraic expressions \(3a - 4b + 4c\), \(2a + 3b - 8c\), and \(a - 6b + c\), we will follow these steps:

### Step 1: Write down the expressions
We have three expressions:
1. \(3a - 4b + 4c\)
2. \(2a + 3b - 8c\)
3. \(a - 6b + c\)

### Step 2: Group like terms
We will group the terms based on their variables:
- **Terms with \(a\)**: \(3a\), \(2a\), and \(a\)
- **Terms with \(b\)**: \(-4b\), \(3b\), and \(-6b\)
- **Terms with \(c\)**: \(4c\), \(-8c\), and \(c\)

### Step 3: Add the coefficients of \(a\)
Now, we will add the coefficients of \(a\):
\[ 3a + 2a + 1a = (3 + 2 + 1)a = 6a \]

### Step 4: Add the coefficients of \(b\)
Next, we will add the coefficients of \(b\):
\[ -4b + 3b - 6b = (-4 + 3 - 6)b = -7b \]

### Step 5: Add the coefficients of \(c\)
Finally, we will add the coefficients of \(c\):
\[ 4c - 8c + 1c = (4 - 8 + 1)c = -3c \]

### Step 6: Combine all the results
Now, we combine all the results from the previous steps:
\[ 6a - 7b - 3c \]

### Final Answer
The sum of the given algebraic expressions is:
\[ \boxed{6a - 7b - 3c} \]

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