A 290.0 mL buffer solution is 0.300 M in acetic acid and 0.300 M in sodium acetate.Part AWhat is the initial pH of this solution?

Because [HAc ] = [Ac-], the pH will equal pKa of acetic acid, or [H+] = Ka for acetic acid. If you look at the expression for Ka for acetic acid:

Ka = [H+][Ac-]/[HAc], if [Ac-] = [HAc], then Ka = [H+].

Using the Henderson-Hasselbalch equation:
pH = pKa + log [Ac-]/[HAc]
Again, if [Ac-] = [HAc], then that ratio is 1, the log of 1 = 0, and pH = pKa.