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How many NOR Gates required to realize the given logical expression?

Y = (A+C)(A+D')(A+B+C')

whether you need 2-input nor gate or 3-input nor gate etc. Please specify number of inputs for each nor gate.

Also, specify, whether inputs are available in complement form or not. For example, whether $\bar{C}$ or $\bar{D}$ can be taken as input of nor gate or we should have to realize it using nor gate also.
2-input NOR Gates and the input are not available in complemented form

This is one possibility. It might be possible that number of gates could be less than this. There is no algorithm to find minimum number of gates.

@ankitgupta.1729 Why there's no algorithm? Means, this problem is undecidable?

You can draw and find the direct or best implementation, as shown above.