To find the value that fills in the blank so that the expression \( 42 + 70 = x(6 + 10) \) is equivalent, we first calculate \( 42 + 70 \):
\[ 42 + 70 = 112 \]
Next, we calculate \( 6 + 10 \):
\[ 6 + 10 = 16 \]
Now, we want to solve the equation:
\[ 112 = x \cdot 16 \]
To isolate \( x \), we divide both sides by 16:
\[ x = \frac{112}{16} \]
Calculating the division:
\[ x = 7 \]
Thus, the value that correctly fills in the blank is \( \boxed{7} \).