Well, when you did the google search it should have listed the ‘Faction Standing Repair Plan’…
‘The Plan’ shows various ways to quickly and easily gain Faction Standing… Being at -4.2 standing with Amarr won’t stop you from accessing the Sisters Of Eve Level 1 Epic Arc… Completing that arc for Amarr will give a nice boost to Faction Standing…
There’s also much quicker ways to boost Faction Standing but it will cost some isk… I’m talking about buying Pirate Dog Tags from Market or Public Contracts and turning them in to the Data Center Agents…
Due to various percentages of Faction Standing being rewarded, the best route to go is first complete Level 1 Faction Agents like the Career Agents, their small reward will actually make big increases to your existing negative standings..
For more info on various Faction Agents and how to access them, I suggest checking out ‘The Plan’…