Concentrated hydrochloric acid is about 12.1 M. What volume of concentrated HCl is required to produce 5500 mL of 0.250 M?

Try this:
M1 x V1 = M2 x V2
The starting molarity (12.1) x the volume (unknown) = New molarity (.250) x the new volume (5.500 Liters). Solve for your unknown - watch your units.

You know that 12.1 M means? It means 12.1 mol per 1000 mL

You need 0.250 mol in 1000 mL of solution.

This also means in 5500 mL, you need (0.250/1000 * 5500) = 1.375 mol.

How much solution of HCl contains that amount of moles?
12.1 mol -> 1000 mL
1 mol -> 1000/12.1 mol
1.375 mol -> (1000/12.1 * 1.375) = 113.636 = 113.6 mL

So, you use only 113.6 mL of concentrated HCl and add water until you get a total of 5500 mL of solution.