Please explain the logic. I am not trying to solve it using trial and error or using any software. I am just looking for the next step. This sudoku is from apple 'Sudoku King' app.
Let's take one more step, with logic.
The green squares are where a 4 could go, based on your pencil marks. Let's establish a series of facts.
1. If a 4 goes in R7C6, then a 4 must go in R9C3 (by hidden single in the bottom-left 3x3 box)
2. By #2, if a 4 goes in R7C6, then there will be 4s in C3 and in C6
3. No more than one 4 may be used in a column (by column-restrictions)
4. Exactly 4 must be used in R6 (by row-restrictions)
5. The possible spots for a 4 in R6 are in C3 and C6
6. By #2, #3 and #5, if a 4 goes in R7C6 then a 4 cannot go in R6. This contradicts #4, therefore a 4 does not go in R7C6
7. By #4 and #6, if a 4 goes in R7C6 then a contradiction arises.
Or, look at this picture:
If R7C6 is a 4, then R9C3 must be a 4 (#1). I have colored in those spots blue. There is now no way to place a 4 in R6's green squares without it being in the same column as an already-placed 4, and two 4s in one column is not allowed (#3).
R7C6 and R9C3 are 9s (R7C6 we just found couldn't be a 4, so it must be a 9, and simple hidden single for the bottom-left 3x3 box determines where its 9 goes)
But from here, there's no way to progress by logic, because there are two solutions. (Thanks to @venus in the comments for alerting me to this!)