Add : `5a+6b-3c, 4b+c-3a and a-6c-3b`.

Answer

To solve the problem of adding the algebraic expressions \(5a + 6b - 3c\), \(4b + c - 3a\), and \(a - 6c - 3b\), we will follow these steps:

### Step 1: Write down the expressions
We have the following expressions to add:
1. \(5a + 6b - 3c\)
2. \(4b + c - 3a\)
3. \(a - 6c - 3b\)

### Step 2: Group like terms
To add these expressions, we will group the like terms (terms with the same variable):
- The terms with \(a\): \(5a\), \(-3a\), and \(a\)
- The terms with \(b\): \(6b\), \(4b\), and \(-3b\)
- The terms with \(c\): \(-3c\), \(c\), and \(-6c\)

### Step 3: Add the coefficients of like terms
Now, we will add the coefficients of the like terms:

1. For \(a\):
\[ 5a - 3a + 1a = (5 - 3 + 1)a = 3a \]

2. For \(b\):
\[ 6b + 4b - 3b = (6 + 4 - 3)b = 7b \]

3. For \(c\):
\[ -3c + 1c - 6c = (-3 + 1 - 6)c = -8c \]

### Step 4: Combine the results
Now, we combine the results from the addition of like terms:
\[ 3a + 7b - 8c \]

### Final Answer
The sum of the expressions \(5a + 6b - 3c\), \(4b + c - 3a\), and \(a - 6c - 3b\) is:
\[ \boxed{3a + 7b - 8c} \]