I think this is a picture before the most recent expansion. (They saw this picture and said "hmm not wide enough, too congested.")

In the normal parts:

• 2 express/toll/HOV/carpool lanes
• 5 regular highway lanes
• 3 feeder lanes (in Texas, the highways tend to have "feeders" or "service roads" or "frontage roads" that run parallel to highways so that people can exit and enter, turn onto intersecting roads, and access local businesses, and Houston calls them "feeders").

That's 10 in each direction. But at any given time there might be merge lanes between the express and the regular lanes, between the highway and the feeder, or between the feeder and a turn lane. So at the widest point, around the major freeway intersection with another huge toll highway, they bump it up to one more of each type of lane, for 13 lanes in each direction.

There's also a fair debate about whether the feeder lanes should count. After all, they have traffic lights and intersections to deal with. But on the other hand, driving on them is necessary to get on and off the highway lanes, so in a sense it's part of the same highway.