New to mountain biking gears

So I just grab a used mountain bike, and I can't seem to shift on the right side(back gears) past 4th. I try to and the lever just goes all the way forward but won't do anything.

Same with the left gear, I can't get to the large gear wheel, just the 2 smaller ones at the front.

I have no idea what I'm doing wrong? I used to ride BMX so I have no idea how all these work. I understand the big gears are for uphill and the small are for staying fast on flat, but am I doing something wrong or is something broke?

Thanks!