You count 74 CFU on a pour plate. The plate was prepared by spreading 0.2 mL of a 1:10,000 dilution of the original sample. What was the density of the original culture (in cells/mL)?

The of the original culture was 4 × 10⁶ CFU/mL.

I presume that you mean 74 CFU (colony forming units).

##"74 CFU"/"0.2 mL sample" × "10 000 mL sample"/"1 mL original"##

= ##4 × 10^6"CFU/mL of original solution"##

Note: The answer can have only 1 significant figure, because that is all you gave for the size of your aliquot. If you need more precision, you will have to recalculate.

The formula I find in my searches is

"##"CFU" × "dilution factor" × 1/"aliquot" = "CFU/mL"##"

Then ##74 × 10 000 × 1/0.2 =4 × 10^6 " CFU/mL"##

It gives the same numerical answer, but it requires memorization.