To solve this expression, we need to follow the order of operations (PEMDAS/BODMAS).

First, let's simplify the expressions inside the parentheses:

46^7 - 7^5 = 4,084,901,000,000 - 16,807 = 4,084,884,192,193
16^8 - 4^16 = 65,536 - 4,294,967,296 = -4,294,901,760

Now, let's substitute these values back into the original expression:

(4,084,884,192,193) * (-4,294,901,760) : (12^4 + 14^2)

Next, let's simplify the denominator:

12^4 = 20,736
14^2 = 196

Now, let's substitute these values back into the expression:

(4,084,884,192,193) * (-4,294,901,760) : (20,736 + 196)

Now, let's simplify the numerator:

(4,084,884,192,193) * (-4,294,901,760) = -17,559,724,318,647,856,203,520

Now, let's substitute this value back into the expression:

-17,559,724,318,647,856,203,520 : (20,736 + 196)

Now, let's simplify the denominator:

20,736 + 196 = 20,932

Now, let's substitute this value back into the expression:

-17,559,724,318,647,856,203,520 : 20,932

Finally, let's divide the numerator by the denominator:

-17,559,724,318,647,856,203,520 ÷ 20,932 = -838,860,800,000,000,000