To solve the equation \( \frac{4}{1} (12r - 8) = 6r + 10 \), let's start by distributing the \( \frac{4}{1} \) (which is simply 4) to the terms inside the parentheses:
\[ 4(12r - 8) = 6r + 10 \]
Distributing 4 gives:
\[ 4 \cdot 12r - 4 \cdot 8 = 6r + 10 \]
This simplifies to:
\[ 48r - 32 = 6r + 10 \]
Next, we want to get all the \( r \) terms on one side and the constant terms on the other. First, subtract \( 6r \) from both sides:
\[ 48r - 6r - 32 = 10 \]
This simplifies to:
\[ 42r - 32 = 10 \]
Now, add 32 to both sides:
\[ 42r = 10 + 32 \]
This simplifies to:
\[ 42r = 42 \]
Finally, divide by 42:
\[ r = \frac{42}{42} \]
Thus, we find:
\[ r = 1 \]
The value of \( r \) is \( 1 \).