Installing New Cartridges

I have entered into at least the 3rd level of plumbing hell, starting with a simple "Honey Do" request to stop the hot water bathroom sink faucet from dripping. I am unable to reattach and correctly orient the handles for the right side. I am a total novice, and I observe there are only two orientations for the cartridge since in has two notches that correspond the notches on the flange (not sure if I am using the right word, see pics)

Looking at the notches that will accept the tangs on the cartridge, it looks like the hot and cold are oriented differently. Hot water side is at about a 1 and 7 on the clock, while the cold is at about 10 and 4. I don't see any easy way to reorient the flanges. I have worked and worked with the hot side, and cannot get the correct orientation for turning on and off. Thanks.

Can you show a picture of the bottom of the handle. And also one looking straight down into the hole?

Sure. Thanks for responding Jeff.

The cartridges have a tab to orient them . The handles should be parallel to the wall at the "off" position and pull toward you to turn on. Some cartridges are either hot or cold, some you just rotate it 180 degrees to make it work correctly. You may have to turn the valve body to line them up perfectly.

What is the "valve body"? So the orientation of the flange as I mentioned is not important?

House Doc said:

The cartridges have a tab to orient them . The handles should be parallel to the wall at the "off" position and pull toward you to turn on. Some cartridges are either hot or cold, some you just rotate it 180 degrees to make it work correctly. You may have to turn the valve body to line them up perfectly.

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I just don't know what I am doing wrong. Here is a pic of the faucet from above in the off position for both hot and cold. For good reason, wife not happy with this. Here also is a pic with the handles off.

The valve body is the opening you are inserting the cartridge into. Normally it tightens from down below. You may have to spin it to get proper orientation.

Work it backwards. Take the old cartridge and put it in the handle and get feel for the orientation. You’ll see how the new cartridge wants to be installed. You can see on and off with that cartridge. Don’t forget to change the seats and springs (it’s probably all you needed anyway.