You need to tell us the objective of the question. You can't just present us with an equation without a question to answer.

I am assuming that the question is to express y in terms of x, which is probably the most logical question to be asked here.

2 lg sqrt (y + 1) = 3 + 4 lg x
2 lg (y + 1)^0.5 = 3 + lg x^4
lg (y + 1)^(0.5 * 2) = 3 + lg x^4
lg (y + 1) = 3 + lg (x^4)
lg (y + 1) - lg (x^4) = 3
lg [(y + 1) / x^4] = 3

Converting to index,

(y + 1) / x^4 = 10^3
y + 1 = 1000 x^4
y = 1000 x^4 - 1

It is not possible to solve any question with 2 variables with 1 equation. Please copy out the entire question instruction for future questions. Eric has approached the question logically.

My apologies for the late reply and giving the whole question.