Please help?

You went from 9 to 6 which means one side was multiplied by 1.5, therefore all other sides were magnified by same amount (1.5), so find the option where the side on the bigger triangle is 1.5 times bigger than the one on the first.
In this care it is C since 4/6 = 1.5 and no other option gives this magnification factor. Similar means size is different and angles are the same so all sides are multiplied by same amount. Which is provable because ratios of sides to other sides like cos and sin and tan are true no matter size of triangle.

Answer: C

In similar triangles, comparing a side of the smaller object and dividing it by the same side of the larger object makes a ratio that should be consistent through the shape. In the triangles drawn, we are told the base is 6 cm and 9 cm, so that ratio is:

6/9 or 2/3

So of the answers, any two lengths of a related side that is also in a 2/3 ratio can be a possible set of lengths. So let's look at your options:

3 and 6. That's a ratio of 1/2, so not the answer.

4 and 5, a ratio of 4/5, so not the answer.

4 and 6, a ratio of 2/3, which matches the original ratio, so this is the answer.

To double check the last answer isn't the solution, the lengths are 5 and 6, a ratio of 5/6, so not the answer.