A flagpole casts a shadow 10 ft long. if a man 6 ft tall casts a shadow 4ft long at the same time of day, how tall is the flagpole?

It is like cross multiplication, which is the actually height over the height it casts.

which is. 6ft. / 4ft. = x / 10ft.

x is the unknown height the flagpole and 10ft is the height of the shadow.

You then cross multiple.

Which will give you

4ft. x = 10ft. * 6ft.

which will give you

4ft. x = 60ft.

so you switched the place of the 4ft. to the oppose side, it will give you : 4ft.

It is : because 4ft. has a variable which is x (can also so be any letter, but I used x instead).

you are now left with

x = 60ft. : 4ft.

x = 15ft.

(15 because 60 : 4 is 15 and ft because you are asked to find how tall the flagpole is in ft.)