The tiles are pushed to the left. When two equal tiles meet, they become one single tile with double the value.
A tile that has just merged does not merge again in the same move. So 2 2 4 8 becomes 4 4 8, not 8 8.
The second question goes the other way - "how many 2s are inside a 128?" A 4 is made of two 2s, an 8 of four, a 16 of eight. Keep halving your way down.
For parents
What does this exercise practice?
The doubling sequence 2, 4, 8, 16, 32 ... gets a picture here. Because every tile visibly grows out of two smaller ones, it becomes clear why the numbers grow so fast - and why a 512 already holds 256 twos.
Common pitfalls
The most common trap is the double merge - 2 2 2 2 becomes 4 4, not 8. Sliding works from left to right, and each tile takes part only once per move.
How to practice at home
Fold a sheet of paper in half as often as you can and count the layers - 2, 4, 8, 16 ... After seven folds there are 128 layers, and hardly any more are possible.
Related: Table of Values, Number Sequence