At level 6, a Sorcerer may have a maximum of 6 Sorcery Points. This is enough to create a level 4 spell slot. Would the Sorcerer be able to create a level 4 spell slot, even though he only knows level 3 spells, in order to cast a spell with a higher slot (such as Fireball to add an extra 1d6 to the damage and make it hard to Counter Spell)?
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The sorcerer's Flexible Casting class feature allows the sorcerer to expend 6 points to create a level 4 spell slot and the sorcerer can use that slot to cast a lower-level spell that he knows.
There is no restriction on creating or using spell slots of a higher level -- the only restriction is that you don't get those slots back on a long rest. On the other hand, if you have the slots, you can use them, even if your current class level doesn't explicitly grant them. Also keep in mind that slots created with sorcery points always disappear after a long rest.
This is further reinforced by the rules for multiclassed spellcasters, quoted below, which state that if you have slots higher than a level you can cast, you can use them for your lower-level spells.
Yes, according to the rules
There is nothing that says that you explicitly cannot create spell slots higher than you normally have available. The Flexible Casting feature states (according to this site):
Since there is no restriction saying that the slots must only be for a level that you normally can cast, the rules seem to allow creating higher level slots than you normally have access to.
Additionally, there is nothing in the PHB Errata correcting this, so I believe that the rules are pretty solid in allowing this.
Personally, as a DM, if a player asked me this question mid-session, I would be a little bit uncomfortable with allowing this, but after reading the rules more closely I'd probably give in since it doesn't seem like a mistake. Additionally, it doesn't seem like too much of a balance issue because the sorcerer is essentially using all of his or her sorcery points for the long rest or burning up a lot of lower spell slots to upcast a spell one level higher than they would normally have access to. It's a pretty high cost for one upcast. This seems to be not only rules-safe, but fairly balance-safe as well.
Yes, as clarified
Sorcerers at level 6 normally only have access up to level 3 spell slots, but can use 6 sorccery points to create a level 4 spell slot.
Likewise, sorcerers at level 7 normally only have access up to level 4 spell slots, but can use 7 sorccery points to create a level 5 spell slot.
As clarified by a tweet from Jeremy Crawford, DnD 5e's rules manager,
Jeremy Crawford @JeremyECrawford:
This should be taken as a clarification from the game's rules manager, but is not considered RAW unless incorporated into a subsequent Sage Advice Compendium published on the WotC website.