What is the formula used to solve the problem: How many milliliters of 1.171 M HCl are required to react with 7.69 grams of CaCO3 ?

It's easier to solve it with several equations.

Write the equation and balance it.
2HCl + CaCO3 ==> CaCl2 + H2O + CO2

Convert 7.69 g CaCO3 to moles. moles = grams/molar mass.

Using the coefficients in th balanced equation, convert moles CaCO3 to moles HCl.

Now convert moles HCl to L.
M = mols/liter
Finally, convert L to mL.