@jimj12 #8 'in such way that the king can not oppose you': in the position in #2 you can go to c4 in three moves, the black king can go to c6 in three moves. Someone who knows these endgames (for example not @todo_pro ) knows that it is then not possible any more to enter the key squares. You can not even enter c5 or d5. The black king opposes you on c6.
But you can also go to a4 in just three moves (see my hint in #4)! While the black king can only go to c6 in this time.
So you count in your mind: 'Kc2-b3-a4 – three moves' and 'Ke7-d6-c6 – also three moves. It is my move now.' You set up this position with wk on a4 and bk on c6 in your mind, and you see: 'I can go to a5, where i am threatening to go to the key square a6. Then i win. Therefore he has to answer Kb7, to prevent me from going to a6. Then i can go to b5 and i have the opposition. if he goes to a7 i can enter key square c6, if he goes to c7, i can enter key square a6'.
But you can also go to a4 in just three moves (see my hint in #4)! While the black king can only go to c6 in this time.
So you count in your mind: 'Kc2-b3-a4 – three moves' and 'Ke7-d6-c6 – also three moves. It is my move now.' You set up this position with wk on a4 and bk on c6 in your mind, and you see: 'I can go to a5, where i am threatening to go to the key square a6. Then i win. Therefore he has to answer Kb7, to prevent me from going to a6. Then i can go to b5 and i have the opposition. if he goes to a7 i can enter key square c6, if he goes to c7, i can enter key square a6'.