Let \( l_1 \) be the line in \( xy \)-plane with \( x \) and \( y \) intercepts \( \frac{1}{8} \) and \( \frac{1}{4\sqrt{2}} \) respectively, and \( l_2 \) be the line in \( zx \)-plane with \( x \) and \( z \) intercepts \( -\frac{1}{8} \) and \( -\frac{1}{6\sqrt{3}} \) respectively. If \( d \) is the shortest distance between the line \( l_1 \) and \( l_2 \), then \( d^{-2} \) is equal to __________.
