Left recursion is eliminated by converting the grammar into a right recursive grammar.
Consider the grammar with left recursion: $A\rightarrow A\alpha/\beta$
Then we can eliminate left recursion by: $A\rightarrow\beta A’,A’\rightarrow\alpha A’/\epsilon$
Consider the given grammar:
$A → Ba / Aa / c$
$B → Bb / Ab / d$
First eliminate left recursion from $A → Aa/Ba / c$ we get:
$A → BaA’ / cA’$
$A’ → aA’ / ∈$
Now the given grammar is:
$A → BaA’ / cA’$
$A’ → aA’ / ∈$
$B → Bb / Ab / d$
Now put the A productions into $B\rightarrow Ab$ we get:
$A → BaA’ / cA’$
$A’ → aA’ / ∈$
$B → Bb / BaA’b / cA’b / d$
now remove the left recursion from B’s production we get:
$A → BaA’ / cA’$
$A’ → aA’ / ∈$
$B → cA’bB’ / dB’$
$B’ → bB’ / aA’bB’ / ∈$