Be careful! Try to figure out why he is crossing out the 6. At about 3:55, Professor Loh says that "as long as I have a multiple of 8 and 9, I will also have a multiple of 6". That's because if a number is a multiple of 8 and 9, it should also be a multiple of 2 and 3, so it's a multiple of 6.
Another way to think about the "crossing out" is to say that: the fact that the number is a multiple of 6 isn't "helpful" or "new" information (we already know the number is a multiple of 6). Can we "cross out" the 8? Actually no, because the 8 provides some very valuable information! The main reason why is that 8 = 2x2x2, and what this says is that the LCM of the 8, 9 and 10 that's left must have three factors of 2. Neither the 9 or the 10 tells us that the LCM needs three factors of 2 (the 10 only says there is at least one factor of 2). This might make more sense later on in the video, when Professor Loh looks at the prime factorization of each of the numbers.
If that didn't make too much sense, maybe think of it like this: If you want to cross out a number, it should be because you already know from the other numbers that the LCM is a multiple of it. If you're thinking about crossing out the 8, but you're not sure if being a multiple of the other numbers (9 and 10) means being a multiple of 8, then you probably can't cross it out, it might be important information.
I hope that helped. Happy learning!