To solve the equation \( 18 : \left( \frac{496}{124x - 6} \right) + 197 = 260 \), we need to follow these steps:

1. Isolate the fraction term.
2. Solve for \( x \).

Let's break it down step by step.

### Step 1: Isolate the fraction term

First, subtract 197 from both sides of the equation:

\[ 18 : \left( \frac{496}{124x - 6} \right) = 260 - 197 \]

\[ 18 : \left( \frac{496}{124x - 6} \right) = 63 \]

### Step 2: Simplify the division

The division symbol ":" can be interpreted as division. So, rewrite the equation as:

\[ \frac{18}{\frac{496}{124x - 6}} = 63 \]

### Step 3: Simplify the complex fraction

To simplify the complex fraction, multiply both the numerator and the denominator by \( 124x - 6 \):

\[ \frac{18 \cdot (124x - 6)}{496} = 63 \]

### Step 4: Simplify the equation

\[ \frac{18 \cdot (124x - 6)}{496} = 63 \]

Multiply both sides by 496 to clear the denominator:

\[ 18 \cdot (124x - 6) = 63 \cdot 496 \]

\[ 18 \cdot (124x - 6) = 31248 \]

### Step 5: Distribute and solve for \( x \)

Distribute 18 on the left side:

\[ 18 \cdot 124x - 18 \cdot 6 = 31248 \]

\[ 2232x - 108 = 31248 \]

Add 108 to both sides:

\[ 2232x = 31356 \]

Divide both sides by 2232:

\[ x = \frac{31356}{2232} \]

\[ x = 14 \]

So, the value of \( x \) is \( \boxed{14} \).