To get the hang of it, follow these steps.  Then later you can shorten the
process.  But at first do it step by step.

(-4xyz)(-2x2∙y3∙z4)

Everything here is multiplication, so put multiplication dots between
every pair of factors, letters and numbers and also between the parentheses:

(-4∙x∙y∙z)∙(-2∙x2∙y3∙z4)

Multiply the numbers -4 times the -2 and get +8 or just 8
Just write the 8 first and eliminate the -4 and the -2

8(x∙y∙z)∙(x2∙y3∙z4)

Write the letters over and over as many times as the exponent says:
That is, instead of x2 write x two times: x∙x
Instead of y3 write y three times: y∙y∙y
Instead of z4 write z four times: z∙z∙z∙z

8∙(x∙y∙z)∙(x∙x∙y∙y∙y∙z∙z∙z∙z)

Since everything is multiplied, you don't need the parentheses,
so eliminate them

8∙x∙y∙z∙x∙x∙y∙y∙y∙z∙z∙z∙z

Arrange the letters in alphabetical order:

8∙x∙x∙x∙y∙y∙y∙y∙z∙z∙z∙z∙z

Count the number of x's. There are 3 of them, so write x3 instead of x∙x∙x

Count the number of y's. There are 4 of them, so write y4 instead of y∙y∙y∙y

Count the number of z's. There are 5 of them, so write z5 instead of z∙z∙z∙z∙z

8∙x3∙y4∙z5

Finally you can erase the multiplication dots if you like.

8x3y4z5

Now you can gradually over time, start shortening the process by skipping steps, but be careful!

Edwin