This kind of position, with fixed pawns and the Kings both in front of their respective pawns (a Knights jump away), is known as "Trebuchet".
Whoever moves loses.
So in the following position, both Kings have to get closer to the pawns on the e-file, but care must be taken to avoid Zugzwang.
If White, for example, tries the direct approach, 1.Kd6, Black responds with 1...Kf5, setting up a zugzwang situation known as the "trebuchet". White's King must give ground, abandoning his pawn.
The correct method for White is to sneak up on Black's pawn by 1.Kd7, forcing Black to defend with 1...Kf5. And now, White steps up with 2.Kd6 setting up a favorable "trebuchet" for himself.
Now it's Black's King who must withdraw, allowing White to capture the e6-pawn, with an easy win.