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 log24) / (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