To find the value of \( b \) that makes the expressions \( (16k + 14) - (13k + 4) \) and \( bk + 8 \) equivalent, we first simplify the left-hand expression:
\[ (16k + 14) - (13k + 4) = 16k + 14 - 13k - 4 \]
Now, combine like terms:
\[ = (16k - 13k) + (14 - 4) = 3k + 10 \]
So, the expression simplifies to:
\[ 3k + 10 \]
Next, we want to set this equal to the right-hand expression, \( bk + 8 \):
\[ 3k + 10 = bk + 8 \]
Now, we can equate the coefficients of \( k \) and the constant terms from both sides.
- From the \( k \) terms:
\[ 3 = b \]
- From the constant terms:
\[ 10 = 8 \]
The second equation \( 10 = 8 \) is not valid; however, we need \( b \) to satisfy the first equation.
Thus, the value of \( b \) that makes the expressions equivalent is:
\[ \boxed{3} \]