The voltage and the current between A and B points shown in the...

The four parallel branches between the common left node $A$ and the common right node are all identical: each consists of a $27\text{ V}$ source in series with a $3\ \Omega$ resistor. In the third branch, the two cells $(14\text{ V}$ and $13\text{ V})$ aid each other, giving a net EMF of $14 + 13 = 27\text{ V}$.

Thevenin equivalent between $A$ and $B$:
Since all four branches have the same EMF and polarity in parallel:
$V_{th} = 27\text{ V}$

The four $3\ \Omega$ resistors in parallel give:
$R_{th} = \dfrac{3}{4} = 0.75\ \Omega$

Load branch (diagonal):
The diagonal connecting $A$ and $B$ consists of two $3\ \Omega$ resistors in series, so:
$R_L = 3 + 3 = 6\ \Omega$

Current through the diagonal branch:
$I = \dfrac{V_{th}}{R_{th} + R_L} = \dfrac{27}{0.75 + 6} = \dfrac{27}{6.75} = 4\text{ A}$

Voltage across $A$ and $B$:
$V_{AB} = I \cdot R_L = 4 \times 6 = 24\text{ V}$

Hence, the voltage is $24\text{ V}$ and the current is $4\text{ A}$, which corresponds to option $(2)\ 24\text{ V},\ 4\text{ A}$.