The sound called /r/ in Japanese is not quite the same sound as the L or R sounds of English. And as you've correctly observed, there's more than one way to pronounce /r/ in Japanese. There are a couple technical terms from linguistics that might help:
- /r/ is considered a phoneme. That means it's considered a single sound, even if it's technically pronounced a little bit differently sometimes.
- The individual pronunciations are called allophones.
With the /r/ sound, there are two main allophones to consider. (The following is based on The Sounds of Japanese by Timothy Vance, page 89):
The first one is the one described in the answer istrasci links to; it's called an apico-alveolar tap, and it's written with the IPA symbol [ɾ]. This sound involves quickly tapping the tongue on the roof of the mouth, specifically on the alveolar ridge (the ridge located behind the teeth). The apico- part of the name means that you use specifically the tip of your tongue, not the blade.
The second one is what Timothy Vance refers to as a non-tap allophone. In this version of /r/, the tongue is already resting on the roof of the mouth, so all you do is pull your tongue off instead of tapping. And this is the allophone you heard in roku. (For whatever reason, Vance chooses not to give this allophone a separate symbol, so I'll refer to it by name instead.)
This non-tap allophone occurs when it's the first sound you say (called utterance-initial position). And that's why you heard it in roku, because she wasn't saying anything before she started to say the /r/ sound. The non-tap allophone also occurs immediately after an /N/ sound, as in the words benri or jinrui.
The tap allophone occurs in any other position, which in Japanese amounts to intervocalic position (meaning between vowel sounds).
Understanding the two allophones described above is important, but there's also some personal variation in exactly how the /r/ sound is pronounced. It varies from speaker to speaker, and it may vary a bit even for a single speaker. Although I described a central tap above, which is written [ɾ], the Japanese /r/ isn't specifically central. It can instead be a lateral tap, which is written [ɺ]. I think it's possible that you may perceive the lateral tap as sounding more like an English L sound.
Unfortunately, I've been unable to find any references that describe exactly when [ɾ] is used and when [ɺ] is used. They're described as being in free variation in Japanese, which means that speakers can use either central or lateral versions of /r/ in any context without it being considered strange or in error. However, it's often true that sounds described as being in "free variation" are not actually selected at random, and I suspect this may be true of Japanese as well.
It's possible that these or other variations in the Japanese /r/ may lead you to think that sometimes it sounds more like L, and sometimes it sounds more like R. That's fine, of course, but it's important that you realize all these sounds are simply one phoneme in Japanese. That is, no matter how you pronounce /r/, it's still mentally /r/ to a native speaker of Japanese. And the more you study Japanese, the more you're likely to feel the same way.
In my opinion, you should focus on learning when to use the tap allophone, and when to use the non-tap allophone. I wouldn't worry as much about the other sorts of variation. If you do that, then I think the idea of an L versus R contrast in Japanese will disappear for you, and before long, it'll just be /r/ to you, too.