To multiply mixed numbers, we first convert them to improper fractions, then multiply the fractions, and finally, simplify the result if possible.
-2 2/3 can be written as an improper fraction:
-2 2/3 = -(2*3 + 2)/3 = -8/3
-4 3/7 can be written as an improper fraction:
-4 3/7 = -(4*7 + 3)/7 = -31/7
Now we can multiply the two fractions:
(-8/3) x (-31/7) = (8/3) x (31/7) = 248/21
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 1:
248/21
Therefore, -2 2/3 x (-4 3/7) = 248/21.