Translation:The cakes my mother makes are tasty.
The second set of characters has 的. Both sets of character have the same meaning. In this case use of 的 is personal preference. When it is a close personal relationship you do not need to use 的.
我的老师 我老师 both are: my teacher
她的爷爷 她爷爷 both are: her grandfather
I think it was explained in the module 'family 1'
This sentence is trying to test the Chinese equivalent of an English relative clause, which your sentence does not have. Your sentence moves the relative clause in such a way that the subject of the sentence changes (from cakes to mother) as does the main verb (from are to makes), and consequently the predicate changes from an adjectival one (tasty) to an object of the main verb (delicious cakes).
Your sentence, written in Chinese, is 我妈妈做很好吃的蛋糕。" The same characters, in a different order. Notice the descriptor of 蛋糕 (which is now 很好吃) no longer contains an action verb.
The 的 links the phrase preceding it to the noun following it. So, in this sentence, 我妈妈做 ("my mother made [it]") is used to describe 蛋糕 (the cake). In English, we would put the descriptive phrase after the noun ("The cake that my mother made"), but in Chinese, it comes before the noun ("The my-mother-made-[it] cake").
I used the singular 'cake' also.
I ran the characters through an online translator, the results were:
'My mom made a good cake'.
When I ran the English answer (from above) through the translator the results were the characters provided.
It appears this phrase could be taken either way.
No one ever says in English a cake is "tasty".
We might say however that a cake tastes good. Tasty is usually reserved for savoury (non-sweet) food, like tasty meat or a tasty dish, but not a sweet sugary cake.
They should replace it with delicious or something more like "The cakes my mother makes taste good".
Well the people who work at Disney use the word tasty to describe cakes.
Serve up a slice of Disney magic with this tasty cake recipe featuring its very own hidden Mickey!
There is also a US brand called "tastykake" which is a play on "tasty cake."