In a parallelogram, the sum of adjacent angles is 180 degrees. Therefore, we can set up the equation for angles B and D as follows:
\[ (4x - 18) + (2x + 42) = 180 \]
Now, simplify this equation:
\[ 4x - 18 + 2x + 42 = 180 \]
Combine like terms:
\[ (4x + 2x) + (-18 + 42) = 180 \] \[ 6x + 24 = 180 \]
Next, subtract 24 from both sides:
\[ 6x = 180 - 24 \] \[ 6x = 156 \]
Now, divide by 6:
\[ x = \frac{156}{6} = 26 \]
Since none of the options (60, 20, 10, 30) match 26, it appears there might be some discrepancy with the choices provided. Please double-check the provided answers or the problem. However, based on the calculations, the value of \( x \) is \( 26 \).