Distribute both sides:

$4(2w + 3) = \frac{1}{2}(-4w + 9)$

$8w + 12 = -2w + \frac{9}{2}$

Add $2w$ to both sides:

$10w + 12 = \frac{9}{2}$

Subtract 12:

$10w = \frac{9}{2} - 12 = \frac{9}{2} - \frac{24}{2} = -\frac{15}{2}$

$w = -\frac{15}{20} = -\frac{3}{4}$