If R1 = 6 Ω, R2 = 8 Ω, R3 = 2 Ω, ε1 = 4 V, and ε2 = 14 V, what is the current in R

In a parallel circuit, the voltage across one branch is the same as the total voltage across the circuit. so the E is same. Hence R is the total resistance of the circuit. 1/R=1/R1+1/R2+1/R3

=1/6+1/8+1/2=19/24

R=0.7917 ohms