The low side mosfets will work fine with 6v to the gate but driving the upper mosfets with 6v is going to cause problems.
In a N-mosfet bridge, driving the upper mosfets with the same voltage level as the drain voltage (6v in this case) will overheat them because they will operate in a semi-conductive state.
When you apply 6v to the gate of the upper mosfet then you apply a Vgs of 6v BUT as soon as the mosfet starts to conduct the voltage at the source rises (becomes more positive) and as it rises Vgs gets lower and lower (since Vgs is referenced to the source and not the ground) until the mosfet reaches a balance. That balance point is related to the Vgs-th and will keep the mosfet in a half open state.
There are two forces that keep this balance, if the mosfet tries to conduct more then the source will become more positive and Vgs will decrease, if on the other hand it tries to conduct less then Vgs will increase.
To avoid this problem with a N-mosfet as a high side switch you must either use an isolated power supply that will be applied between source and gate and will add over the existing voltage or a higher voltage from the one that is connected to the drain (if not available it can be generated with a bootstrap circuit).
Since you have 6v to the gate it would be a good idea to use about 6v+5v to the gate of the upper mosfets. A 12v source would be very convenient if available.
Another option is to use P-mosfets as high side switches in the bridge.
A level translator using a single transistor (non inverting action) is like:
simulate this circuit – Schematic created using CircuitLab
And there is also the mosfet solution (also non inverting)
simulate this circuit