I wonder how got his driver’s license.这句话对吗?

不对.
如果是“我奇怪他怎么获得驾照的”,那么后半句缺主语,应该为：
I wonder how he got his driving license.
如果是“我想知道怎么取得驾照”：
I wonder how to get a driving license.
如果是“我想知道要怎么拿（偷）他的驾照”：
I wonder how I can get his driving license.