Answer: $226$

Explanation:

$1$ . Simplify the first equation:

   - Start with $\dfrac{1}{4}(s + 4t) = 544$ .

   - Multiply both sides by $4$ to clear the fraction:

     $s + 4t = 544 \times 4$

     $s + 4t = 2176$ (Equation 1)

$2$ . Prepare the system for elimination:

   - We have the system:

     1) $s + 4t = 2176$

     2) $7s - 8t = 1192$

   - We can eliminate the t-variable if we multiply Equation 1 by $2$ .

     $2(s + 4t) = 2(2176)$

     $2s + 8t = 4352$ (New Equation 1)

$3$ . Use the elimination method:

   - Add the New Equation 1 and Equation 2 together:

     $(2s + 8t) + (7s - 8t) = 4352 + 1192$

     $9s = 5544$

   - Solve for s:

     $s = \dfrac{5544}{9}$

     $s = 616$

$4$ . Solve for t:

   - Substitute the value of s ( $616$ ) back into the original simplified Equation 1:

     $616 + 4t = 2176$

   - Subtract $616$ from both sides:

     $4t = 2176 - 616$

     $4t = 1560$

   - Divide by $4$ :

     $t = \dfrac{1560}{4}$

     $t = 390$

$5$ . Calculate the final required value:

   - The question asks for the value of $s - t$ .

   - $s - t = 616 - 390 = 226$

$6$ . Conclusion:

   - The value of $s - t$ is $226$.