We can suppose that whether or memory is good or not depends

从逻辑看这是病句,正确的表达是
We can suppose that whether we have good memory or not depends to an extent on our state of happiness.
上面我加了 to an extent （在一个程度上） 使句子比较客观.
happiness 不是 bad memory 的唯一促使原因,因此说 to an extent 比较客观.
state of happiness 幸福状态
但从语法看两个句子都对（虽然原句表达欠佳）.

不奇怪，句子没错。是宾语从句中又带了一个主语从句。你打错了一个字:
We can suppose that whether our memory is good or not depends on our happiness.
还可用一个形式主语it，把主语从句后置:
We can suppose that it depends on our happiness whether our memory is good or not.