By applying Logarithmic formula we can get the answer.

Let X = (log24 x log16)/ (log2 x log 2) - (log192 x log 12)/ (log2 x log2)

Now breaking equation into parts we get

X = (log2*12 x log2^{4}) / (log2 x log2) - (log12*16 x log12) / (log2 x log2)

Now we know that logMN = logM + logN, SO solving we get

X= {(log2 + log12) x 4log2} / log2 x log2 - {(log12 + log16) x log12} / log2 x log2

= 4 - (log12 x log12)/ log2 x log2

= 4 - 12

X = -8